One great power of nearly any god, is that he can somehow "exist" outside of Space Time.
Problem; existence occurs only in space time. Tell me if you disagree.
Meaning if a god isnt in space (which virtually spans for an infinite distance), and doesn't act over time (which is close friends with space), where could it possibly be?
Well, I don't want to argue for the existence of God, however I am not sure about your premise. What about space/time itself? Surely that (a) exists and (b) is not 'within' itself.