Big bang isn't proven
In science nothing is ever proven. There is no such thing as "proof by observation/demonstration". All you can say is that a theory is consistent with observations/demonstrations, allowing one to be reasonably confident that you're on solid ground.
And no, I'm not being anti-Big Bang. The same applies to gravity et al. In theory gravity applies to all objects with mass. The observation that brick released from hand falls on toe does not prove gravity, it merely demonstrates it. Perhaps there is some mass out there that is immune to gravity and the reason we cannot find it (and why it does not amass into planets) is because it needs gravity to form into planets and we use gravity to detect mass.
The Big Bang is just a model. A model (a parable for people in white coats) draws together various observations and theories and makes them seem consistent (I say seems because I have not personally checked out Big Bang and I expect there are some out-of-focus bits that need hand waving to explain).
Before we get all uppity and defensive of science, it is worth noting that science goes through phases of making up models, finding a lot of support for those models, then finding a weak spot and watching those models crumble.
For example, up to approx the 1960s, plate teutonics was rubbished by the scieeeentists of the day as a very stupid idea, yet we (mostly) accept plate teutonics now (40-odd years later) and look back at the pre-teutonic folk as if they were flat-earthers.
It is really naive to think that many of our pet theories of today won't get trashed within the next 50-odd years. To think otherwise would suggest we've reached as far as science can - that would be a sad thought.