If we are to treat the word “proof” as an absolutism with a “beyond shadow of doubt” standard then the word becomes useless. If “proof” cannot happen then what is the point of having a word to describe a completely nonexistent state of things?
As a practical matter at some point strong evidence should (and does) provide sufficient confidence that something is true to regard and treat it as “proven.” When the evidence establishes the odds of the question having another answer are so small that it no longer makes sense to continue to consider it the sensible thing is to regard it as “proven” (unless something dramatic comes along) so you can move on to other things.
I don’t think science requires us to be obsessed with minuscule uncertainties as to be paralyzed with indecision. Otherwise we end up debating whether the Earth is flat. I know some people actually believe it is, but I see no value in treating such things as legitimate questions.