I don't see where the OP asks specifically about Catholicism, other than the tag on the post. Anyway, I will provide some insight here, from a non-denom standpoint (I suppose?)
To upfront answer the question, it is valid to say Jesus is the God of the Old Testament, because Jesus is God. Unlike the Mormon answer also here, God to my non-denom faith, and even Catholic upbringing, is One God, albeit in different forms.
First, the messiah is revealed throughout the old testament, and makes several appearances Himself. However, the writers of the old testament weren't keen to the developments that occurred in Paul's time, so the actual nature of a trinitarian God are hinted at, but never actually referenced (the puzzle wasn't complete yet). The Bible is story-like in that sense, the early actors weren't aware of the climax, even though the pieces were available to them at the time, or at least they didn't have the appearance of Jesus and the Holy Spirit to put it altogether and make a case for a trinitarian Godhead.
The Son of Man, as Jesus often referred to Himself, appears in Daniel 7:
13 “I was watching in the night visions, And behold, One like the Son
of Man, Coming with the clouds of heaven! He came to the Ancient of
Days, And they brought Him near before Him. 14 Then to Him was given
dominion and glory and a kingdom, That all peoples, nations, and
languages should serve Him. His dominion is an everlasting dominion,
Which shall not pass away, And His kingdom the one Which shall not be
Jesus confirms this during the passion, from Matthew 26:
63 But Jesus kept silent. And the high priest answered and said to
Him, “I put You under oath by the living God: Tell us if You are the
Christ, the Son of God!”
64 Jesus said to him, “It is as you said. Nevertheless, I say to you,
hereafter you will see the Son of Man sitting at the right hand of the
Power, and coming on the clouds of heaven.”
A lot of people then argue that perhaps the "Son of Man" doesn't explicitly make a case for Him being also the Son of God. However, by law at the time, in Leviticus, the case is made for a blood-relative to redeem sold possessions (or even persons) by a family member.
25 ‘If one of your brethren becomes poor, and has sold some of his
possession, and if his redeeming relative comes to redeem it, then he
may redeem what his brother sold. 26 Or if the man has no one to
redeem it, but he himself becomes able to redeem it,
48 after he is sold he may be redeemed again. One of his brothers may
redeem him; 49 or his uncle or his uncle’s son may redeem him; or
anyone who is near of kin to him in his family may redeem him; or if
he is able he may redeem himself.
By becoming human, fulfilling the Son of Man prophesy in Daniel, Jesus is able to redeem us by His blood. Jesus is foretold as early as Genesis 3:
14 So the Lord God said to the serpent:
“Because you have done this, You are cursed more than all cattle, And
more than every beast of the field; On your belly you shall go, And
you shall eat dust All the days of your life. 15 And I will put enmity
Between you and the woman, And between your seed and her Seed; He
shall bruise your head, And you shall bruise His heel.”
Enmity here being salvation and the conquering of sin and thus death. Jesus is from the seed of Eve, and He accomplishes this on the Cross. God became man to fix the problems we made for ourselves in the garden on that day.
As for appearances, you can argue "the Angel of the Lord" is an early, non-human, incarnation of Christ, because this particular Angel, whom the people in the OT who experience Him state they experience God Himself, ceases to make appearances in the NT, post-Christ.
Jesus says in John 8 that He was around before Abraham:
58 Jesus said to them, “Most assuredly, I say to you, before Abraham
was, I AM.”
To Moses (Exodus 3), God declared Himself as "I AM." Jesus does the same thing here. Also note in Exodus 3, "the Angel of the Lord" was present.
2 And the Angel of the Lord appeared to him in a flame of fire from
the midst of a bush. So he looked, and behold, the bush was burning
with fire, but the bush was not consumed.
Judges 2, the Angel of the Lord speaks in such a way, as God does.
2 Then the Angel of the Lord came up from Gilgal to Bochim, and said:
“I led you up from Egypt and brought you to the land of which I swore
to your fathers; and I said, ‘I will never break My covenant with you.
2 And you shall make no covenant with the inhabitants of this land;
you shall tear down their altars.’ But you have not obeyed My voice.
Why have you done this?
We know that Angels do not speak as a literal mouthpiece to God (like His voice echoes through them), actually, Angels deliver messages on behalf of God. This Angel, however,
speaks in the first person, as God Himself. For example, Gabriel to Mary, in Luke 1:
30 The angel told her,
“Don’t be afraid, Mary. You have found favor with God.
Genesis 32, Jacob wrestles with the a MAN, which is later called an Angel (but yet, God Himself):
24 Then Jacob was left alone; and a Man wrestled with him until the
breaking of day. 25 Now when He saw that He did not prevail against
him, He touched the socket of his hip; and the socket of Jacob’s hip
was out of joint as He wrestled with him. 26 And He said, “Let Me go,
for the day breaks.”
But he said, “I will not let You go unless You bless me!”
27 So He said to him, “What is your name?”
He said, “Jacob.”
28 And He said, “Your name shall no longer be called Jacob, but
Israel;[b] for you have struggled with God and with men, and have
29 Then Jacob asked, saying, “Tell me Your name, I pray.”
And He said, “Why is it that you ask about My name?” And He blessed
30 So Jacob called the name of the place Peniel:[c] “For I have seen
God face to face, and my life is preserved.”
Hosea 12:4 confirms this as "the Angel:"
Yes, he struggled with the Angel and prevailed; He wept, and sought
favor from Him. He found Him in Bethel, And there He spoke to us—
There's a lot more, actually. But I think this demonstrates somewhat clearly that Jesus is God, and God revealed Himself throughout the Old Testament.
Think you could wrestle with God and tell about it? :)