You're right... that always boggled my mind. If God occupies infinity, then he was there for infinity before us (twiddling his thumbs?), which you might interpret to mean he's never caught up with us! Our universe has a beginning, and it's "The Big Bang". According to quantum physics, there could be multiverses, and our universe is the result of a star exploding to create a black hole (imploding into the black hole but exploding on this side) and we're on the other side of it. We have a beginning; we have a time-line. Our universe is not infinite, and so God could not have possibly been there "forever" before us.
So, like you said, it would make more sense that God came into being at the same time our universe did, and hung out creating and destroying stars/planets until however many billions years ago that our planet came into being. But uh... all that sounds stupid. There is no need for there to be a god... in any universe.
This is about as likely as a unicorn jumping out from behind a bush and yelling "Ride me!". As such, I simply can't tell you what my reaction would be.
I'd like to be flippant about it, but in all honesty, if a god in "all his power" appeared before me, I figure it'd be pretty scary and I'd probably be prostrate in two seconds flat. However, if it was just a guy with a beard in a sheet wearing sandals, I'd say "prove it".
Your question has alerted me to the disappointing fact that I don't own a bazooka. When did I lose sight of my dreams?!