Some of the answers above are outstanding. But, I think fail to delineate between two critical points:
Religion - does the question want proof of a religion, Christianity, possessing truthful facts?
Relationship - does the question want proof of the reality of experiencing a relationship with the Living God of the Christian Bible and walk of life?
Almost all the writings above are on intellectual ascent, though a few slight touches about relationship. And, the answers above concede you don't really get proof via intellectual ascent. This is correct.
However, the relationship aspect in the above answers is
underdeveloped - yet it is the only proof offered by God.
In the interest of #2, I would offer another answer:
1. Character Witness
For starters, scripture is a character witness. You either accept it as that or you are off on the intellectual paths mentioned above.
A character witness is used by God, because He will not bow to an inferior way of life. With God, you can count on His character and His proficiency/competence/skill. Therefore, demands like proof, validating and vetting are for inferior ways of life where the concern is fallibility or malevolent intentions. There is no such thing with God, e.g.
"in Him is no darkness at all", 1 Jn 1:5 & many verses
"For with God nothing will be impossible.", Lk 1:37 & many verses
Including providing an infallible character witness through fallible beings inspired to write and canonize scripture.
God's not using intellectual prowess, nor requiring it, rather deliberately avoiding it:
"when I came to you, did not come with excellence of speech or of wisdom declaring to you the testimony of God.", 1 Cor 2:1
it pleased God through the foolishness of the message preached to save those who believe.", 1 Cor 1:21
Character witness is founded on relationship: you put confidence or assurance in one's character and ability. Intellectual ascent is quite another foundation. While men are without excuse observing nature (Rom 1:20), that is a completely different matter to experiencing the reality of God in a personal relationship.
God's purpose with mankind is a personal relationship. The experience of that relationship is the only proof offered by God.
Most approach God differently,
"but of the tree of the knowledge of good and evil you shall not eat,
for in the day that you eat of it you shall surely die.”, Gen 2:17
This verse is not a call to abandon God-given intellect and reason. Rather, it is a warning that relying on it, "feeding" on it - one eats to stay alive - will lead to death. Life is found only in the Person of Jesus Christ Who -is- God. God offers proof through a Person - one you personally experience in reality.
2. Little Children
"Let the little children come to Me, and do not forbid them; for of
such is the kingdom of heaven.”, Matt 19:14
Note 'do not forbid them'. God will not forbid a person approaching Him - relationally - as a little child.
Children lack considerable experience and knowledge. They are limited and dependent on a higher up. They are vulnerable, but generally born trusting.
Regarding intellectual ascent, God has no need of natural ability. He can make donkeys talk, turn kings into cud-chewing animals, grants natural ability via fiat and opens and closes understanding at-will. Intellectual capacity is at best a catalyst to start seeking Him - relationally.
A seeker must come to a deep realization he/she is limited and in need, like children, but also flawed, broken, weak, subjective and, like a little child, cannot help him/herself. This is called 'missing the mark' or "sin":
"for all have sinned and fall short of the glory of God", Rom 3:23
We have all deeply offended God by our nature. If one can't be moved by this fact to the point of completely changing one's life proof will never come. This is repentance. Furthermore, it is God that enables us to repent! That is based on one's disposition in approaching Him.
Here's where proof starts via a personal transformation beyond what any other means could do. These are very personalized per seeker, because God is now engaging and manifesting an experience - via personal relationship. Religion can only testify, but not prove. (Back to character witness ;-)
Now, atheists and agnostics abound with high moral character. But, they don't experience God beyond all doubt, because morality isn't the enabler. They didn't seek God, acknowledge their sin; therefore, they have no relationship with Him and, thus, no (starting) proof.
Another obstacle to proof is religion.
"For Satan himself transforms himself into an angel of light", 2 Cor 11:14
This goes well beyond conventional Catholicism vs. Protestantism vs. non-denomination and other doctrinal derivatives. Well beyond it.
This is why I asked #1 and #2 above, because this is a fact:
Christianity is not ekklesia.
There's overlap and mingling, but they are not the same thing. That's very offensive to many in Christianity. Let the Lord sort it out, just follow Him first and foremost before any preacher, teacher, etc. He is real. He speaks. And, removes all doubt of needing proof.
Satan will settle for anyone between you and Christ, including a well-meaning devout Christian. Only One Man could say, "the ruler of this world comes, but he has nothing in Me" (Jn 14:40). The rest of us, he has something in us, fallen nature. Mainstream Christianity rarely matures Christians, because the onus is on the believer to seek the Lord past the so-called inner court, where feeding on showbread (preachers, teachers, publications) is the highest ground of most. You go alone into the Holy of Holies just like the High Priest modeled. Personal relationship.
"If a man loves Me, he will keep my words: and My Father will love him, and we will come unto him, and make our abode with him.", Jn 14:23
'Keep my words' means to continue, persist, abide continuously. Doing this, especially against deep internal conflict and external adversity, God lives inside a person removing all doubt whatsoever. Intellectual ascent has no hope of this level of transformation. Likewise comfortable living. Without the transformation there is no further proof.
"do you not know that your body is the temple of the Holy Spirit who is in you, whom you have from God, and you are not your own?", 1 Cor 6:19
Many get initial experiences, but to keep those experiences going you must catch the last part of that verse, ...
'you are not your own'
You're all in or you're all out. The Lord calls the shots (Matt 7:21), determines your place in the Body of Christ (1 Cor 12:18) and determines your inheritance (Ps 47:4). Here's where natural ambition cuts off further proof. And, where religion obscures experiencing relationship with Christ resulting in a testimony to observers how impotent religion really is.
"Many will say to Me in that day, ‘Lord, Lord, have we not prophesied
in Your name, cast out demons in Your name, and done many wonders in
Your name?’ And then I will declare to them, ‘I never knew you;
depart from Me, you who practice lawlessness!’", Matt 7:22-23
That's the Christian religious. 'Lawlessness' isn't just the Ten Commandments, it's natural ambition and there's plenty of it in Christianity.
You must invite the Holy Spirit into every part of your person and life - all of it - nothing left out. Christ is a gentleman, He never forces Himself on anyone. You are about to find out what offends God so much in your nature! Everyone has 'soul blockers' like mentioned above: your emotions, will, biases, brokenness, etc. that prevent the will of the Holy Spirit from operating. This is where you die to self day-by-day, yielding to the invitation you grant the Holy Spirit.
Make no mistake about it: God is going to reduce that part of you to ashes, killing it, literally. You will experience the literal death of self - if you want proof on a regular basis by hearing Him, His interventions, His manifestations. (You will not lose your personality and individual uniqueness in this process).
This doesn't fill the pews and offering plates, though. So, Christianity comes up with all kinds of programs around this. Prosperity gospel is true, but in context God wants to prosper you by transforming your nature, not preserving the natural man or its interests. This means you die to this life, not gain more of it.
"Be ashamed, you farmers, Wail, you vinedressers", Joel 1:11
These are teachers being rebuked by the Lord when the Day of the Lord comes. Scripture is full of rebuke of religion, and that religion is most certainly Christianity as generally practiced. Christianity is not ekklesia.
God is not a tyrant denying you a living, but He most certainly has no interest in preserving any of it at the expense of maturity. His interest is quite the opposite, to reduce you to ashes. The burnt offering was all in, reduced to ashes, nothing was left out. Nothing less was acceptable to the Lord.
Most of Christianity is stuck above, struggling to yield and being distracted and deceived from maturing. One example, is teachers keeping the same students for decades. They failed to mature students when Christ stated His goal with every believer:
"But the anointing which you have received from Him abides in you, and
you do not need that anyone teach you; but as the same anointing
teaches you concerning all things, and is true, and is not a lie, and
just as it has taught you, you will abide in Him.", 1 Jn 2:27
"None of them shall teach his neighbor, and none his brother, saying,
‘Know the LORD,’ for all shall know Me, from the least of them to the
greatest of them.", Heb 8:11
Following mainstream Christianity is not maturing most in it.
Maturity costs you everything. Including going against the crowd knowing "with most He is not well pleased" (1 Cor 10:5).
"narrow is the gate and difficult is the way which leads to life, and there are few who find it.", Matt 7:14
"Strive to enter through the narrow gate, for many, I say to you, will seek to enter and will not be able.", Lk 13:24
"I die daily.", 1 Cor 15:31
"but its swamps and marshes will not be healed", Ez 47:11
Few mature, because it costs you everything:
- c.f. the burnt offering. All-in or not acceptable.
- c.f. the grain offering: seeds are crushed into fine flower = the old nature is broken or not acceptable.
- c.f. precious stones: long-term heat and pressure to the point you are changed into something you weren't starting out.
Not being able is due to the seeker hanging on to something against the Holy Spirit's will. This is always associated with the death of the old nature and giving up this life's interests. Christianity has hardly done that en masse. Little wonder so many Christians still want to hear more from God and experience Him. They're stuck in religion, not relationship with Christ.
Few get to this level of proof. God hides it in a personal relationship as proof. Only a testimony, a character witness, is visible to the world.
Christ seeks a bride. Just like He made marriage an analogy, e.g. sexual intercourse is very personal, intimate, you don't share that with anybody. Ditto the mature seeker's experience of Christ in a real, living personal reality. God's not sharing that with observers and certainly not the world. It's His and the seeker's alone.