The fact that something did happen is proof that it can happen. In reality, it is the only actual proof, as everything else is speculation. We may believe all sorts of things, but only those that we know have happened are proven to be possible (or proven otherwise).
So, how do we know that something happened ? Either we observed it ourselves and remember it, or someone else observed it and told us about it.
Considering the well-known shortcomings of both human observation and human memory as well as the tendency of each of us to turn our reports of events into narratives that may well leave out or spin various details, our knowledge rests upon shaky ground. And if our knowledge is less reliable than we think, then what does that say about proof ?
Science, with it’s logic and math, offers a way out of this situation, as it provides ways to test what we believe and compare our results with others. Results that are reproducible (other people can get the same things to happen when they apply the same conditions and actions) are the closest that science comes to claiming that something is proven. This is why science is so important: without fully-functional science, very little is known in any useful sense of the word.
Of course, even scientists can not deal with too much uncertainty in everything, so the tendency is to accept some so-far-not-disproven theories as if they were proven and proceed accordingly. This tendency is made more likely when money and power and influence get involved and steer scientists toward their own goals.
True science is never about orthodoxy, accepted wisdom, and the trappings of power and influence. True science is about an outlook toward reality that says “let’s see if we can figure out testable theories for how things work and then test them” and it is about that continual quest for HOW as much as it is for WHAT.
When new theories that do a better job of explaining observed reality come along and show the flaws in the accepted wisdom, this is given all sorts of names (paradigm shift, among others) that really boil down to “oops! We assumed something was proven when it was not.”