No, that's not the same question at all. God could mean a polytheism as I described. It could mean some kind of pantheism where God is one and the same as nature, impersonal. But the God you describe is an intelligence that existed prior to the universe and created it of it's own will.
So, the real question is not where did the universe come from? The real question is was the cause of the universe intelligent?
By invoking an intelligent cause, what you are actually doing is making your explanation less probable, you see, because you're positing a cause that is complex.
The atheist simply posits that the universe came into being via some mechanism, they don't try to define the mechanism as anything more than a cause, but the theist posits that first a complex intelligence came into being that in turn caused the universe and in doing so create a paradox.
If an intelligent origin is necessary for existence, then that intelligence must itself have an intelligent origin. If God does not have an intelligent origin, then there is no need for God.
Thus, if God does not have an intelligent origin then the theist accepts the concept of something (God) coming into being of it's own accord, or always having existed without an origin.
This in turn nullifies the idea that for something to exist, it needs an intelligent cause, thus making the atheist's original position viable. Not only that, but because the atheist's position is the simpler (there are less steps and variables) Occam's Razor suggests it is the more likely of the two theories to be correct.