The Big Bang theory does NOT claim that the universe is not timeless; in fact, quite the opposite. The theory suggests that time would not have existed prior to the Big Bang, but all the quarks that became all the matter and energy in the universe always existed, they were simply held together in a point in space by their own gravity. We have reasonably understanding of this sort of phenomenon since it is in most respects quite similar to a black hole. The argument is that the entire contents of the universe were contained within the effective equivalent of one massive black hole. This is not a perfect description, but it's close enough. Then at some point the Big Bang occurs and the quarks are blasted out in all directions, based on essentially a random fluctuation. There are, in fact, well-respected physicists who believe that there have been multiple Big Bangs - that ultimately the universe will run out of energy and collapse on itself, then at some point a similar random fluctuation causes another Big Bang, and that this cycle has been repeating itself and will continue repeating itself in perpetuity. Unfortunately the math behind this theory is fuzzy; it's difficult for anyone to explain under any circumstances the accelerating expansion of the universe, which is how we arrive at dark energy. Frankly, nobody knows what dark energy is supposed to be, and the only meaningful evidence for it IS the accelerating expansion of the universe, but it's little better than a fudge factor in the math at this point. Given that we don't well understand the present behavior of the universe and what's driving it, it's difficult to prove or disprove any theory about the long-term fate of the universe, IE will it expand forever until everything is so isolated from everything else that matter no longer interacts, or will it ultimately collapse back into itself. But you certainly can't easily DISPROVE the idea that the universe has cyclically repeated itself, though I think more people doubt this theory than espouse it.