Around 150 years before Athanasius wrote On the Incarnation, Justin Martyr wrote Dialogue with Trypho. As a Christian philosopher, Justin explored the case for Christ through a conversation with a Jewish seeker named Trypho. As the conversation unfolds the need for the cross is affirmed.
The rest of this post contains excerpts from chapters 89-95 from CCEL.
Then Trypho remarked, “Be assured that all our nation waits for Christ; and we admit that all the Scriptures which you have quoted refer to Him. … But whether Christ should be so shamefully crucified, this we are in doubt about. For whosoever is crucified is said in the law to be accursed, so that I am exceedingly incredulous on this point. It is quite clear, indeed, that the Scriptures announce that Christ had to suffer; but we wish to learn if you can prove it to us whether it was by the suffering cursed in the law.”

Justin the Philosopher by Theophanes the Cretan [Public domain], via Wikimedia Commons
But if these are to be characteristic of Him and mark Him out to all, how is it possible for us to do anything else than believe in Him most confidently? And will not as many as have understood the writings of the prophets, whenever they hear merely that He was crucified, say that this is He and no other?”
“Bring us on, then,” said [Trypho], “by the Scriptures, that we may also be persuaded by you; for we know that He should suffer and be led as a sheep. But prove to us whether He must be crucified and die so disgracefully and so dishonourably by the death cursed in the law. For we cannot bring ourselves even to think of this.”
“You know,” said I, “that what the prophets said and did they veiled by parables and types, as you admitted to us; so that it was not easy for all to understand the most [of what they said], since they concealed the truth by these means, that those who are eager to find out and learn it might do so with much labour.”
They answered, “We admitted this.”
…
you suppose that He was crucified as hostile to and cursed by God, which supposition is the product of your most irrational mind. For though you have the means of understanding that this man is Christ from the signs given by Moses, yet you will not; but, in addition, fancying that we can have no arguments, you put whatever question comes into your minds, while you yourselves are at a loss for arguments whenever you meet with some firmly established Christian.
…
[Through the brazen serpent] He proclaimed the mystery, by which He declared that He (Jesus) would break the power of the serpent which occasioned the transgression of Adam, and [would bring] to them that believe on Him … salvation from the fangs of the serpent, which are wicked deeds, idolatries, and other unrighteous acts.
…
“For the whole human race will be found to be under a curse. For it is written in the law of Moses, ‘Cursed is every one that continueth not in all things that are written in the book of the law to do them.’ And no one has accurately done all, nor will you venture to deny this; but some more and some less than others have observed the ordinances enjoined. But if those who are under this law appear to be under a curse for not having observed all the requirements, how much more shall all the nations appear to be under a curse who practice idolatry, who seduce youths, and commit other crimes? If, then, the Father of all wished His Christ for the whole human family to take upon Him the curses of all, knowing that, after He had been crucified and was dead, He would raise Him up, why do you argue about Him, who submitted to suffer these things according to the Father’s will, as if He were accursed, and do not rather bewail yourselves?