It depends, and even then it depends. It depends first upon whether we ever discover our massive misconceptions. If not, then I imainge we'd continue along merrily piling fancy details upon them. But if (as I think you are imagining) we one day discover that we've gotten it all wrong, then what happens depends upon the inclination of the discoverers, and their culture. There would be shell-shock, certainly, and perhaps some desire to keep heads in the sand and continue on oblivious to the truth. But it's difficult to live by claims we know to be false--try it sometime. And we humans have a genuine built-in urge to understand the way our world works--some say it's what distinguishes us from the other animals. So in all likelihood, we would soon embark upon fresh attempts to understand the way the world actually works--new experiments, new theories, and new conceptual frameworks. I hereby propose, though, that an independent commission be established to determine how on earth we got everything wrong. And a second one, comprised of philosophers, to determine whether this is really even possible.
Well, I've answered other similar questions despite my not being terribly well-informed about science, so I'll take a stab at this one, too.
The answer to this question depends partly upon whether the universe is "open" or "closed", that is, upon whether the expansion of matter will eventually cease, the universe will start contracting, and everything will end in a "Big Crunch". If so, then it is my understanding that the energy so generated would lead to another Big Bang, and the whole process would start again. If that's how things are, then, before the Big Bang, that may have been how things were.
So suppose things weren't like that. Then I believe current physical theory implies that there wasn't any "before the Big Bang". Astronomers start counting time with the beginning of the Big Bang because time itself began with the Big Bang. If that seems bizarre, well, the theory of relativity does have a way of upsetting one's everyday assumptions about time.
Someone who knows more about this than I do care to confirm or deny?
The following comment has been kindly sent in by Professor Kannan Jagannathan (Department of Physics, Amherst College):
"The best evidence we have for the isotropy andhomogeneity of space leads cosmologists to hold that the universe hasno center and no periphery. If the universe is infinite now, it was soat the Big Bang, and the bang occurred everywhere (in such a case, thedensity of the universe would have been infinite at BB); if theuniverse is finite (and unbounded) now, it was probably point-like atBB, but it is not to be thought of as embedded in some larger space. That was all there was as far as space was concerned; it was'everywhere' then, and is everywhere now.
In the standard model of cosmology, as well as inmost variants of it, the initial rate of increase of the scaleparameter (crudely, the radius of the universe, or the rate ofexpansion of space) would have been bigger, perhaps much bigger, thanthe speed of light. The combination of these two points would suggestthat if light was emitted at BB, we would still be receiving bits ofthat light from parts of the universe that had sped away too fast, andwe would continue to do so for the foreseeable future, particularly ifany of the inflationary scenarios is taken seriously.
The reason the earliest light is from something like300,000 years after the BB is because that is when the universe hadcooled enough to allow neutral atoms to form, and the universe suddenlybecame transparent to electromagnetic radiation. Prior to thisso-called 'recombination era' (a misnomer since it was the first timethat the 'combination' could have occurred), the universe was opaque toall 'signal carriers' that we can think of or detect easily; if onegoes a little farther back in time than 300,000 years, even theneutrinos would have scattered too much to be available as a faithfulimprint of events before."
I think most scientists would reject an assumption in your question — that they believe the Universe needs to be one way or the other. Theories in science do not say how matters must be, they describe how they are.As to why scientists think the Universe does have a beginning, well,presumably it's because that hypothesis best fits the availableastronomical data. If you want the details, talk to yourlocal physicist.