Wouldn't the center be the Big Bang and the 3D Universe at the current time (if Relativity lets me write about a current time) be the 3D surface of the 4D sphere (or spheroid) that the Big Bang is creating by keeping to expand?
There's really no way to know if there was something in existence before the big bang however. We just lack evidence of such a thing.
It is true that in GR you can't speak of "before" the big bang, but the big bang itself is a feature within time. It happens at the first moments of time and everywhere in space. And if you replace the initial singularity with a dense quantum foam and thus are able to extend time into the past in some quantum sense, the big bang doesn't go away.