Not only isn't it proven, but it's failed every one of its unique predictions and continually needs the invention of unobserved entities (dark energy, dark matter) to explain away its failed predictions. Yet you get downvoted for some reason. In any other scientific discipline, if your hypothesis predicted that the speed of the expansion of space should be slowing down (even granting that space can expand, which is probably the first incorrect interpretation of evidence that sent us down this path) and observations show things speeding up that would be the end of the hypothesis. Instead, we invent a magical form of energy that has just the properties we need to cause the acceleration because we all know the hypothesis MUST be true so this entity must exist... which is EXACTLY the way religious folks justify making things up during debates, because they KNOW in the end they must be right.

When your hypothesis ends up with clusters of galaxies that would have taken longer to form (if gravity were the only force shaping the clusters' formation) than the age assigned to the universe(!), an honest application of the scientific method would demand rejecting the hypothesis.

When your hypothesis needs at least one separate adjustable parameter to predict the abundance of each element lighter than lithium, that just might be a sign your hypothesis doesn't actually predict anything at all.

When your hypothesis needs 90% of the matter in the universe to be made of something undetected, you just might have a problem.

When the hypothesis predicts equal amounts of matter and anti-matter in the universe, not observed and not explained, that's another sign your hypothesis is a failure.

When the galaxy shows large-scale structure out to more than 1Gpc in opposite directions, there's more structure than an explosion can account for and another sign your hypothesis is a failure.

I could go on, but just as the world looks nothing like what we would expect it to look like if a benevolent intelligent designer were in charge (Earth has no special place, universe harsh, planet 3/4 water and not habitable in many spots, good and bad things happen at random, etc.), every observation we have of the universe looks nothing like what the Big Bang hypothesis predicted when we have been able to make the observations. Originally Big Bang hypothesis backers expected a completely homogenous universe at greater distances and deceleration. Instead, we have a universe with over 13 observed "walls" of galaxies and voids in between as far as we've been able to observe, and acceleration if the redshift indeed indicated space expansion. It simply looks nothing like an explosion and we've gone on to postulate dark matter and dark energy among other things to try to account for every failed observation, just as religious folk have attempted to co-op evolution and DNA into intelligent design "theory", etc. The reality is the Big Bang hypothesis (it certainly is not a theory with its poor track record) is an adjustable parameter-filled mess that hasn't scored ONE prediction beyond what its predecessors did (Steady State got the same things right the Big Bang did and without the need for adjustable parameters).

Folks who proclaim their allegiance to the Big Bang without ever seriously questioning it are no different than those who believe their religion without ever giving any thought to it. In their minds they're buying into the tactics of people like Frank Turek, who in his book and debates seeks to implicitly make the argument that if you can't explain the existence of everything today with science than God-done-it. It's alright for us as atheists and as supporters of the scientific method to say that we probably don't know the origin of the universe right now. A little over a hundred years ago we didn't know the secret of powered flight either, but that didn't mean that angels could fly.