The theory of causal inference tells you how to do this -- what is the nature of the relationship between correlation and causation? When can we draw conclusion

The theory of causal inference tells you how to do this -- what is the nature of the relationship between correlation and causation? When can we draw conclusions from natural experiments? There is actual rigorous theory that has very clear answers to this. The conceptual tools are powerful. Pearl's "Book of Why" may be a good starting point as a popularization, although sometimes Pearl is not so easy to read. And Pearl presents his own perspective on causal inference only -- there are other schools and techniques, although there are generally equivalences between them. It is definitely possible to understand the core ideas as a layman, if you have a mathematical grasp of basic probability. If you want to go a little further, understanding linear regression helps too. The problem is that actually applying the theory to draw causal conclusions on real-world data seems to be a very subtle and difficult process and even experts who specialize their entire careers in causal inference frequently make mistakes and disagree with each other. So I think a lot of humility is warranted.