Christianity follows up with the claim that God reveals his existence to us -- which relieves us as individuals from the problem of evidentiary proof. Christianity also claims that God reveals His will to us, and that the Bible represents a compilation of revelations.
Be that as it may, the role of God in this argument is as the source of truth. To wit: given that we cannot demonstrate the proof of our assumptions, the only way we know they're true is if some unassailable authority tells us that they're true.
A close approximation is where things always reveal themselves the same to us, e.g., the sun warming the earth. We can't know it's true, but we can pretty much plan our lives as if it were, no all knowing authority is needed.
This is also an assumption and without proof.
As is this: "Christianity also claims that God reveals His will to us, and that the Bible represents a compilation of revelations."