Interesting question. I understand the constraints of the system to be the laws of physics. It would be interesting to see if these would be the same if we ran the Big Bang over and over. It's hard to know how many universes are possible when you only have the one example.
But I suspect that's not the question or the answer you intended. The "created" is a real clue.
"God did it" just raises more questions for me. Where did He come from? If you say he's eternal, or "exists outside of time," or whatever, that's as unsatisfying as anything else being eternal or outside of time or whatever.