“He it is that was crucified before the sun and all creation as witnesses, and before those who put Him to death: and by His death has salvation come to all, and all creation been ransomed. He is the Life of all, and He it is that as a sheep yielded His body to death as a substitute, for the salvation of all, even though the Jews believe it not.” (On the Incarnation of the Word, chapter 37).
“For the Word, perceiving that no otherwise could the corruption of men be undone save by death as a necessary condition, while it was impossible for the Word to suffer death, being immortal, and Son of the Father; to this end He takes to Himself a body capable of death, that it, by partaking of the Word Who is above all, might be worthy to die in the stead of all... For being over all, the Word of God naturally by offering His own temple and corporeal instrument for the life of all satisfied the debt by His death. And thus He, the incorruptible Son of God, being conjoined with all by a like nature, naturally clothed all with incorruption, by the promise of the resurrection.” (On the Incarnation of the Word, chapter 9)
I also came across this article corroborating my conclusions: The School of Alexandria and Athanasius