I will start by stating that this is a very good question, that I am glad that a Jew dared to post it in CSE, and that I upvoted it. I am familiar with the subject because I discussed it extensively last year with a Noahide in a forum on classical theism, and recently I consolidated and expanded my posts on the subject and published the result as part of a broader paper on Academia.edu [1].
Introduction
First of all, it is necessary to address an issue that is implicit in these expressions used in the question: "that same God that they knew", "the same god", "that very same god of the OT", etc.: By "God" we refer to the one absolutely infinite (in perfection, not in spatial extension), absolutely simple, eternal and immutable Subsistent Being, Who created from nothing and sustains in existence everything that exists outside Himself. This must be the starting point, and it is from this starting point that one then determines whether the super-human entity which interacted with the Israelites was God (always meant in the above sense from here onward) or a lesser, created entity.
Clearly the entity identified himself as God when he gave his name in Ex 3:14-15, both in its 1st person form, "Ehyeh", "I Am", and in its 3rd person form, "Yahweh", "He causes to be" (assuming hiphil stem from theophoric names). But that self-identification does not prove, just by itself, that the entity talking to Moses was indeed what it claimed to be. Moreover, neither the plagues nor any other sign or portent performed by the entity on route to Mt. Sinai, in Mt. Sinai, or on route to Canaan proves, just by itself, that the entity performing those signs or portents was indeed God. Which is why I have been referring to the entity in lower case till now.
In order to ascertain that the entity self-identifying as "I Am" and guiding the Israelites out of Egypt was indeed God, one must have previously adopted the postulate that God will not allow a created super-human entity, i.e. a demon, to deceive human beings by performing signs or portents while posing as the one true God. Thus, while God may allow demons to perform signs or portents to lead pagans to worship one or more gods of a polytheistic pantheon, because none of those gods was conceived as the one and only absolute Subsistent Being that created and sustains in existence everything outside Himself, it is against God's philosophically knowable goodness towards humans that He may allow a demon to perform signs or wonders to lead people into believing that the demon itself is the one and only God. (A well-known purported revelation supposedly superceding Christianity, claimed to come from the one and only true God, poses no problem as it did not involve any sign or portent).
The philosophical basis for postulating that God would not allow that people be deceived in a wholly undetectable and unsurmountable way is that such a course of action would be incompatible with the care He shows for people by creating ex nihilo each spiritual soul when the person is conceived. The reasoning goes like this:
Ability for abstract thought implies that each human being has a spiritual soul.
A human spiritual soul cannot emanate from God since He is immutable and absolutely simple (and so cannot let fall drops/sparks which forget that they are part of Him!) It also cannot proceed from the parents' spiritual souls or emerge from matter. Therefore it must be created ex nihilo directly by God, Who alone has the power to create ex nihilo. (In terms of the 3rd-person and 1st-Person forms of the Name, "He causes to be" presupposes "I Am".)
The fact that God creates ex nihilo the spiritual soul of each human person when that person is conceived implies that God cares about human beings, so that He will not allow that they be deceived in a wholly undetectable and unsurmountable way.
As an aside, I am rejecting Marcionism or gnosticism, either in its Sethian or Valentinian flavors, and their views of the God of the OT as a lesser demiurge, either evil or just ignorant, purely on philosophical grounds of classical theism:
Contra Marcionism and gnosticism, only the Subsistent Being can create ex nihilo.
Contra gnosticism, the Subsistent Being is absolutely simple and immutable, not a pleroma within which changes go on and from which parts get out and then back in.
The point of the above is to show that one must start from a solid philosophical position in order to discern whether a sign or wonder is intended to lead people to the one true God or away from Him, and that the reservations on the value of Jesus' resurrection as proof that He is indeed what He claimed to be can also, and much more strongly, be raised on the value of the signs and portents performed on the Exodus, because those signs and portents provide much less apologetic evidence than the resurrection of a man, as any angel can kill but only God can bring back to life. Therefore, a Jew questioning the apologetic evidence of Jesus' resurrection (assuming that it was factual) leaves himself without no principled reason to accept the apologetic evidence of the signs and wonders during the Exodus (assuming again that they were factual).
1. Definition of Revelatory Epistemological Position (RELP)
RELP: The set of criteria that a person holds to be appropriate for determining whether a purported medium of divine Revelation is actually so. (Or in the case of a particular sign or wonder, whether it certifies that the associated revelation comes from God or it does not).
To note, the contents of divine Revelation according to a revelatory tradition can include a consequent revelatory epistemological position. Thus for any revelatory tradition T there are two related revelatory epistemological positions:
The antecedent epistemological position which is required for a person to be able to arrive to explicit propositional faith according to tradition T: R4T-ARELP (Required for T - Antecedent Revelatory Epistemological Position);
The consequent epistemological position which is part of explicit propositional faith according to tradition T: T-CRELP (T - Consequent Revelatory Epistemological Position).
2. Statement of the antecedent epistemological position required for Christianity
The Required for Christianity - Antecedent Revelatory Epistemological Position (R4C-ARELP) must necessarily include the following:
A first postulate based on infinite divine goodness:
ARELP.P1. God will perform a miracle that requires the exercise of God's own exclusive power (as opposed to allowing an angel to exercise its own natural power) - in scholastic terms, a miracle which can happen only if God performs it directly as its only cause, not as its primary cause cooperating with a natural secondary cause, whether material or angelic, - hereafter called "a miracle which only God can perform", only to lead people to truth and good.
plus two corollaries of P1:
ARELP.C1. The possible instances of the "sign or wonder" supporting the claims of the false prophet predicted in Deut 13:1-5 do not include miracles which only God can perform, but are limited to the works that an evil angel can perform by its own natural power when allowed by God.
ARELP.C2. If God performs a miracle which only He can perform through the intervention of a prophet P, God will be certifying in front of everyone that all that P has said and done as prophet so far has God's "seal of approval" and therefore is true and in accordance with God's will, respectively.
plus a second postulate based on metaphysics:
ARELP.P2. The resurrection of a human being is a miracle which only God can perform, regardless of whether God performs it through the intervention of a human being, such as prophet Elisha (2 Ki 4:32-35).
plus two further corollaries from P2 and C1 and C2, respectively:
ARELP.C3. The possible instances of the "sign or wonder" supporting the claims of the false prophet predicted in Deut 13:1-5 do not include the resurrection of the false prophet himself to a glorious state.
ARELP.C4. If God resurrects a prophet P to a glorious state, God will be certifying in front of everyone that all that P has said and done as prophet up to his death has God's "seal of approval" and therefore is true and in accordance with God's will, respectively.
plus a third postulate based on infinite divine wisdom and goodness:
ARELP.P3. If God confers his "seal of approval" to the words and deeds of a prophet P by resurrecting him to a glorious state, He will also provide the means to ensure that the words and deeds of said prophet can be known with accuracy and certainty along time and across space. Because it would be against divine wisdom and goodness for God to give us certainty that whatever P said and did was true and good while not giving us certainty about what P actually said and did!
3. Study of a possible Jewish Consequent RELP which is incompatible with the R4C-ARELP
A possible Jewish consequent revelatory epistemological position would be incompatible with the antecedent revelatory epistemological position required for Christianity if and only if it comprised the following two postulates:
J-CRELP.P1. The Torah (or TaNaKH) contains, explicitely or implicitely, all truths about God and his design, so that any proposition about God or his design which is not in the Torah (or the TaNaKH) and cannot be deduced from it is necessarily false and points to a false god.
J-CRELP.P2. The possible instances of the "sign or wonder" supporting the claims of the false prophet predicted in Deut 13:1-5 include any miracle that only God can perform, and specifically the resurrection of the false prophet himself to a glorious state.
Calling a generalized version of P1 "Revelation Completeness", RC, and a generalized version of P2 "Full Divine Power at the service of lie", FDPsl, there are four possible combinations of the affirmation or negation of each postulate:
(¬RC, ¬FDPsl): The I-CRELP of Biblical Israel, according to Christianity
(RC, ¬FDPsl): The C-CRELP of the Church after the death of the last Apostle, according to Christianity
(¬RC, FDPsl): Not allowed because of undecidability
(RC, FDPsl): The possible J-CRELP studied in this section
Next I will show why negating RC (P1) at the same time as affirming FDPsl (P2) leads to undecidability. If one negates Torah (or TaNaKH) completeness, then the Nicene doctrine of a consubstantial Trinity and the Chalcedonian doctrine of the Incarnation of a divine Person are compatible with the Torah (or TaNaKH) and therefore can be the actual case. But even if a divine Trinity is the actual case, the claim by a concrete individual that he is the incarnated Son of God can be true or not, so that in the latter case he would be an impostor and a false prophet. But if one holds FDPsl, a miracle of any kind performed through the intervention of that individual, or even to that individual such as resurrecting him to a glorious state, can be interpreted either as certifying the truth of his words or as supporting the claims of a false prophet. Therefore it is impossible to decide whether a concrete individual claiming to be the incarnated Son of God and showing miracles of any kind in support of his claim is really the incarnated Son of God or an impostor.
3.1. Demonstration that the Biblical Israelite faith does not imply J-CRELP.P1 but actually implies that it is false
1.1. It neither is in the Torah (or TaNaKH) nor can be inferred from it.
1.2. It is intrinsically null regarding further revelation of truths or addition/deletion/change of commandments by God Himself.
1.3. It is positively contradicted regarding further revelation by Isaiah 48:6b-7:
I proclaim to you new things from this time, even hidden things which
you have not known. They are created now and not long ago; and before
today you have not heard them, so that you will not say, ‘Behold, I
knew them.’ (Is 48:6b-7)
1.4. It is positively contradicted in practice regarding commandments by Ezekiel chapters 40-48.
3.2. Demonstration that the Biblical Israelite faith does not imply J-CRELP.P2 but actually implies that it is false
2.1. It neither is in the Torah (or TaNaKH) nor can be inferred from it.
2.2. It is most illogical per Deut 4:34-35, which states that the signs and wonders performed by YHWH to free Israel from Egypt are the evidence on the basis of which Israel may know that YHWH is God, the only God:
Or has a god tried to go to take for himself a nation from within
another nation by trials, by signs and wonders and by war and by a
mighty hand and by an outstretched arm and by great terrors, as the
LORD your God did for you in Egypt before your eyes? To you it was
shown, that you might know that the LORD, He is God; there is no other
besides Him. (Deut 4:34-35)
If the signs and wonders performed by YHWH to free Israel from Egypt are the evidence on the basis of which Israel may know that YHWH is God, the only God, it can be most reasonably inferred that the sign or wonder that YHWH will provide to support the claims of the false prophet of Deut 13:1-5 will NOT involve a greater degree of exercise of divine power than the degree involved at the signs and wonders performed at the Exodus. It is most illogical to think that YHWH will provide MORE apologetic evidence for Israel to believe in a false god than the apologetic evidence He provided for Israel to believe in Himself!
From the above, and from the fact that the signs and wonders performed at the Exodus - the plagues, including the death of all Egyptian firstborns, the parting of the waters, the fire, smoke, lightning and thunder at mount Sinai, - are all events that can be produced by an angel, good or evil, out of his own natural power if allowed to do so by God, it follows that the sign or wonder that YHWH will provide to support the claims of a prophet enticing Israel to go after other gods will be restricted to that kind of events and will not include any miracle which only YHWH can perform.
2.3. Independently from the previous point, it is most illogical regarding the specific signs and wonders performed by Jesus per Isaiah 26:10-11,19; 29:13-14,18-19; 35:2c-6a; 42:6-8. Because it is most illogical to think that God, having promised in the TaNaKH that He Himself would perform specific kinds of signs and wonders to show his own glory, would perform the very same specific kinds of signs and wonders to support the claims of a false prophet enticing Israel to go after false gods!
2.4. Independently from the above points, it is most illogical regarding the passion, death and resurrection of Jesus per Isaiah 51:9-10; 52:10; 53:1 and the rest of chapter 53.
Recalling that the OT expression for the divine power is "God's arm", the prophet starts by asking the arm of the LORD to wake up:
Awake, awake, put on strength, O arm of the LORD; awake as in the days
of old, the generations of long ago. Was it not You who cut Rahab in
pieces, Who pierced the dragon? Was it not You who dried up the sea,
the waters of the great deep; Who made the depths of the sea a pathway
for the redeemed to cross over? (Is 51:9-10)
The prophet does not seem to be asking the arm of the LORD to awake in order to do wonders at the service of falsehood and evil, does he? Because he is asking the arm to awake "as in the days of old", when the Lord did wonders to lead his chosen ones to truth and good. The answer to the prophet's request is in the next chapter:
The LORD has bared his holy arm in the sight of all the nations, and
all the ends of the earth shall see the salvation of our God. (Is
52:10)
Clearly, that "the LORD has bared his holy arm" means that He has performed a work that only He can perform. And the purpose of that work is that "all the ends of the earth shall see the salvation of our God", not to support the claims of a false prophet.
The specifics of that work are detailed in the next chapter, beginning with another mention of God's arm:
Who has believed our message? And to whom has the arm of the LORD been
revealed? (Is 53:1)
Which begins the fourth song of the Servant of YHWH, Who "was cut off out of the land of the living" (53:8), "was assigned a grave with the wicked, but was with a rich man in his death" (53:9), and yet "if He would render his soul as an offering for guilt, He will see His offspring, He will prolong His days" (53:10), "out of the anguish of his soul he shall see light and be satisfied" (53:11). This prophecy about "the Righteous One", the Servant of the LORD, being executed, buried and risen from the dead is the revelation of what specifically the LORD would do when He "bared his holy arm in the sight of all the nations".
3.3. Conclusion
I have demonstrated above that both postulates J-CRELP.P1 and J-CRELP.P2 are false in the framework of the Biblical Israelite faith. Thus, since the Nicene doctrine of a consubstantial Trinity and the Chalcedonian doctrine of the Incarnation are compatible with classical theism and with the Torah or TaNaKH, once J-CRELP.P1 is abandoned, ascertaining the historical truth of the resurrection of Jesus is all that a Biblical Israelite needs to ascertain the truth of Christianity.
[1] https://www.academia.edu/39982502/Proposal_of_a_conceptual_framework_for_the_epistemic_path_to_faith_and_application_to_the_path_from_Judaism_to_Christianity
