It depend on your definition of proof...

Q :How science has accepted there was a big bang ?

A: they found traces of it ? the have not seen it but they have traces of it, as cosmological radiation, redShift(Expanding universe) ...

For me the proof is not essentially what we see, sometimes we can not prove the existence of something with sight, we use critical thinking.

Here is my view:

In science we admit the causality, . The cause of the event was itself caused by a prior cause, which was affected by a previous cause, and so on back.

Because we can not continue to an infinite cause-event we must admit the principle of the original cause and uncaused First Cause (like the who push the first domino ).

This is an important argument that make us believe that there is external (out of the univers) force who made that.

If we think of this force we must admit that this force is space-time independent and immaterial.

there is another scientific argument: The fine tuning ... (I know that the atheist try to disprove this by making new theory of Multi-verse , even if there is multiverse the question still the same where they come from.

So Stop pretending that science is on the side atheist