A recent article in New Scientist posited the idea that the big bang was really a bounce.
It details a computer simulation, based on Loop Quantum Theory, that runs time backwards to the big bang, which demonstrates a bounce back to a previous(ly collapsing) universe. This is apparently one up on general relativity, which breaks down at the big bang.
Having only completed undergraduate physics and maths, the article will take some time for me to absorb properly. But there is a certain neatness to the concept of a universe continuously expanding and collapsing. I would imagine that in that case, there would be no state memory retained from the previous incarnation, so all prior information/knowledge (both about and within the prior universe) would be lost. There is sufficient unevenness to the expansion after a big bang that successive universes would not develop identically.
I have previously drawn a depiction of how time could work going backwards to the big bang. It's a conceptualisation, rather than based on hard physics. The above theoretical paradigm would be closer to hard physics, but still just theory at this point.
In the process of conceiving a universe running backwards to the big bang, most people might imaging a large box, with the matter filling a decreasing amount of space in the middle of the box. Fewer would imagine space as being a contracting 'box', with nothing 'outside' it, because it's hard to think of a space without automatically extending one's thoughts beyond the limits. Likewise with time. Is 'what happened before the start of time' a valid construct?
There is no certainty yet, but I think the ultimate solution would have a satisfying neatness and symmetry.