"That specific God" is the God the supposition asserts that we both might agree on. Not that we would, but that we might for the sake of argument.
Surely you've gotten these kinds of questions before, Professor.
May I call you Shirley?
Does this mean you are going to make me President? I promise to carry out God's plan. Trust me.
Oh, you want me to suppose that I believe in *your* God. Yikes. The Presbyterian God is the one who (according to them) told my Dad's fellow Ulstermen that they should burn Catholic families out of their homes. Since we were Catholic, we were a bit sensitive about that.
Now, it seems, he's moved from arson back to stoning.
Nope, I think if your god were the only one available, I'd still be an atheist. Denial is preferable to depression.