Things like a cyclic universe are not really contradictions of the Big Bang, but more like modifications of it. And yes, that is how they arrive at conditions in the early universe—by going backward in time and extrapolating based on current conditions. But so far the results and predictions tend to agree that the universe was once small, hot, and dense. Nothing in science is a fact, however. It’s a theory.
I’m in agreement. It’s a theory... A well supported one, in fact, but not beyond question by reasonable and intelligent people.