Science isn't about formal and absolutely certain proofs. That's why we have things like the 5 Sigma standard for evidence in physics. We come up with a plausible theory, then look for evidence that it makes useful predictions. No experimental verification can be truly absolute though. Also consider the fact that Newtonian mechanics was superseded by Relativity, and that even though relativity and Quantum Mechanics are thoroughly verified across many domains they are also inconsistent with each other in some ways.

We don't have absolute knowledge in Physics, or science generally in the strict sense that this video and philosophers of logic discuss. We only have useful theories that describe the world very closely to reality across most situations.

We also very importantly get to conclusively rule out an awful lot of ideas and theories. That's very important work. It is all about levels of confidence though. If you think about it, you probably already knew all this, you just hadn't considered the consequences yet. We're all in that boat about a lot of things. I'm afraid in the grand scheme of things, despite all out truly incredible accomplishments, it's also true that we're stuck with fairly limited mental faculties.

As to why? Well, we need to feed and clothe our children somehow. That means figuring out how to get stuff done. Working out explanations of the world that verifiably work, more or less, has turned out pretty well for us.