Well you can only logically rationalize the consistency of a premise, so it's kind of pointless. So if the premise is that god exists, then you're going to logically rationalize that.

Maybe a better way is to explain why god exists. Why would things that it's explaining would make so much sense if god did exist.

But you can't prove it either way.

So you might want to stop hiding behind "logic" and just admit that it's always going to be an uncertain belief. But another pesky thing is that a belief could also be wrong