I've had a lot of people tell me that in order to understand the Orthodox view of the atonement, one must start with the Orthodox view of the incarnation. At first, this made little sense to me. However, what little knowledge I had before has helped to make sense of why this is the case. The East sees salvation as the healing of corruption, more in line with a medical analogy whereas the West sees salvation as the acquittal from judgment, more in line with a legal analogy.
As such, how one views sin will inevitably determine how one views salvation from that sin. It is with that background that I began reading On The Incarnation by St. Athanasius. It is broken into many sections, and the sections are each focused on a particular subject.
The first few sections lay the groundwork for discussing the Son of God as the savior of Mankind, namely in that He is God incarnate. This principle requires two things: that the Son be (a) God, and (b) incarnate as Man.
From the get-go, St. Athanasius does not mince words:
the Word of the Father is Himself divine, that all things that are owe their being to His will and power, and that it is through Him that the Father gives order to creation, by Him that all things are moved, and through Him that they receive their being.---Section 1, On The Incarnation
I can't help but hear the words of the Apostle Paul from Acts 19, "In him, we live and move and have our being." The words commonly referred to Zeus, but Paul used them to speak of Christ. St. Athanasius delivers a similar point: Christ is at the center of creation, both enabling and empowering all that exists.
the first fact that you must grasp is this: the renewal of creation has been wrought by the Self-same Word Who made it in the beginning. There is thus no inconsistency between creation and salvation; for the One Father has employed the same Agent for both works, effecting the salvation of the world through the same Word Who made it in the beginning.---Section 1, On The Incarnation
In the same way, as Christ is the creator, He is the redeemer. This makes perfect sense. The Fall was not merely Man falling into sin, but it was the entire creation falling into corruption. Just as Christ is the one who created all that is, He is the one who heals all that is fallen. We see this in Scripture as well; Christ redeems us by trampling down death by death, but also at the eschaton, He purifies the cosmos in a grand redemption of all that is.
So the first building block is established. Jesus Christ is divine. We know this because He is the creator. The "God" of "God incarnate" is established by Christ's role in creation.