Okay, did some serious physics-thinking last night. The problem is that we have (at this time) no information from anything earlier than the CMB at 400,000 years after the big bang. And we really (under the Standard Model) know no way to find any.
So first, there may be some artifact(s) that await discovery. If we find some kind of "Big Bang" gravitational waves (something we have tried but not been able to do), then relativity gets yet another big check and we may be able to find where they originated from. BIG IF, though, because by definition the singularity of the Big Bang is beyond the applicability of relativity.
Second, M-brane-string theory (all really just one approach) could end up predicting some Big Bang artifact (an early dimension now collapsed?) which would be verifiable directly or in terms of some later behavior (like magnetic monopoles). I did my physics in pre-string days and really am not qualified to prove this statement... it seems possible from very simplified string explanations (equations).
Lastly, a cyclic system (like Penrose and Heller have hypothesized) may leave some artifact (like the subtle circles and ellipses in the CMB). I do not know what artifact could identify a center of expansion, but it might be possible.
All three of those guesses are non-empirical, but rational (metaphysical) only. As far as what science can say at this time (and teach to its practitioners), it is the balloon analogy. Regardless of which of the three structures the universe has (Euclidean, Elliptic, or Hyperbolic--what we think of as geometry, geometry on a sphere, and geometry on a saddle-point) it behaves (and in the far past probably still behaved) like a balloon. Before the Big Bang the balloon was deflated to nothingness. The Big Bang blows up the inside, expanding the outside... the outside is the universe. It came from nothing... no time, no space. The universe is expanding time and space (like the outside of the balloon) which drags along the potentiality that becomes what we see as mass energy (which, in turn changes the space-time).
THIS BALLOON ANALOGY IS A VERY, VERY SIMPLIFIED VERSION OF THE STANDARD MODEL.