Would You Trust The National Academies Of Science To Tell You How Science Works?

That’s just completely wrong. We absolutely have a way of “establishing causation” — or at least of progressively ruling out causes other than our hypothesized cause — which is by disproof of the null hypothesis. In the most common example with which almost everyone is familiar, pharmaceutical companies seeking approval of a drug are required to (at least tentatively) prove its efficacy by disproving the null hypothesis that a placebo is as good or better.