An episode of PBS Space Time provides evidence on why the big bang definitely happened. A later episode then goes on to explain some of the problems with the theory, and the ways it could progress in the future.
We pretty much know for sure that the universe was once extremely small, and extremely hot. And we know that something set it in motion, expanding rapidly and continuing to do-so today. But the actual moment of ‘the Big Bang’ is still a bit of a grey area within physics. The theories of general relativity and quantum mechanics disagree on this pivotal “beginning of time,” and physicists continue to search for an all-encompassing theory to unify the study of our universe.