As you state in the question, the first knowledge given to Adam and Eve of the plan for their redemption is found in Genesis 3:15.
And I will put enmity between thee and the woman, and between thy seed
and her seed; it shall bruise thy head, and thou shalt bruise his
heel. (Genesis 3:15, KJV)
This, being spoken to the serpent (Satan), represented sin. God promised to cause His people, represented by the woman, to hate sin, and to be saved through the "seed" of that woman, representing Christ, the Messiah.
And Moses made a serpent of brass, and put it upon a pole, and it came
to pass, that if a serpent had bitten any man, when he beheld the
serpent of brass, he lived. (Numbers 21:9, KJV)
That serpent represented Christ, who became sin for us.
For he hath made him to be sin for us, who knew no sin; that we might
be made the righteousness of God in him. (2 Corinthians 5:21, KJV)
While that is a New Testament text which Jesus could not have quoted, the symbolism of the following two verses could have supplied its place--with the book of Job having been written by Moses as well.
But I am a worm, and no man; a reproach of men, and despised of the
people. (Psalm 22:6, KJV)
How much less man, that is a worm? and the son of man, which is a
worm? (Job 25:6, KJV)
Virtually the entirety of Psalm 22 is a Messianic prophecy, with special focus on the crucifixion. Jesus may have quoted from it on the walk to Emmaus.
Jesus' words on the cross:
My God, my God, why hast thou forsaken me? why art thou so far from
helping me, and from the words of my roaring? (Psalm 22:1, KJV)
The wounds from the nails predicted:
For dogs have compassed me: the assembly of the wicked have inclosed
me: they pierced my hands and my feet. (Psalm 22:16, KJV)
I may tell all my bones: they look and stare upon me. (Psalm 22:17,
I became also a reproach unto them: when they looked upon me they
shaked their heads. (Psalm 109:25, KJV)
The competition for his garments:
They part my garments among them, and cast lots upon my vesture.
(Psalm 22:18, KJV)
The vinegar and gall:
They gave me also gall for my meat; and in my thirst they gave me
vinegar to drink. (Psalm 69:21, KJV)
Moses also wrote the following reference to the Messiah, called "Shiloh."
The sceptre shall not depart from Judah, nor a lawgiver from between
his feet, until Shiloh come; and unto him shall the gathering of the
people be. (Genesis 49:10, KJV)
Abraham's testing gave further evidence of the Messiah to come, the "Seed" of Abraham.
And Abraham said, My son, God will provide himself a lamb for a burnt
offering: so they went both of them together. (Genesis 22:8, KJV)
And in thy seed shall all the nations of the earth be blessed; because
thou hast obeyed my voice. (Genesis 22:18, KJV)
And, of course, there is always Isaiah 53.
||Isaiah 53: Prophetic of Christ
||He is despised and rejected of men; a man of sorrows, and acquainted with grief: and we hid as it were our faces from him; he was despised, and we esteemed him not.
||Surely he hath borne our griefs, and carried our sorrows: yet we did esteem him stricken, smitten of God, and afflicted.
||But he was wounded for our transgressions, he was bruised for our iniquities: the chastisement of our peace was upon him; and with his stripes we are healed.
||All we like sheep have gone astray; we have turned every one to his own way; and the LORD hath laid on him the iniquity of us all.
||He was oppressed, and he was afflicted, yet he opened not his mouth: he is brought as a lamb to the slaughter, and as a sheep before her shearers is dumb, so he openeth not his mouth.
||He was taken from prison and from judgment: and who shall declare his generation? for he was cut off out of the land of the living: for the transgression of my people was he stricken.
||And he made his grave with the wicked, and with the rich in his death; because he had done no violence, neither was any deceit in his mouth.
||Yet it pleased the LORD to bruise him; he hath put him to grief: when thou shalt make his soul an offering for sin, he shall see his seed, he shall prolong his days, and the pleasure of the LORD shall prosper in his hand.
This passage is very likely one that Jesus would have quoted. It would not have been difficult to connect this passage with the events of Calvary; and Jesus seems to have had a special liking for the book of Isaiah.
But back to Moses, it is worth remembering that the entire sacrificial system which pointed forward to the Messiah was established within the books of Moses.
Surely, to be likened to a snake or to a worm, rather than a man, ignominiously looked upon by the people, bearing reproach, and taking sin itself upon him--these prophecies all foretold the sufferings of the Messiah. The lamb that was slain after sins had been confessed over its head predicted the sacrifice our Redeemer would make in our behalf. Moses foretold a great deal about our Savior through his writings.