I completely agree that you can’t infer causality by “passively” looking at data, in the sense that it sounds like what you’re describing is naively looking at a scatter plot or running a regression of Y on X.

The key insight of causal econometrics is exactly the point you’re making, that in order to understand causality we have to somehow approximate the environment that is present in a lab, where we can randomly assign individuals to treatment and control groups, ensuring that people in both groups are on average the same and thus the only difference in expectation between these groups is the treatment of interest. Of course, we can’t do this with observational data, so we look for natural experiments, or environments where random distribution of treatment may occur among some population by chance.

There are a lot of specific methods, but the essence of them all is that, as long as there is some feature that is as-good-as randomly distributed between people, and that feature is correlated with the treatment we care about, we can use variations in that random factor to estimate the causal effect of changing treatment for those individuals who shift their behavior because of the random variable. An early example in economics is using variation in military participation driven by the Vietnam draft lottery to estimate the causal effect of military participation on lifetime earnings. So in that way, economists really do try to estimate causality by looking for situations in which we might think the “cause” knob is being turned due to historical or institutional quirks.

I’m just skimming the surface, but if you’re interested you should check out Mostly Harmless Econometrics by Angrist and Pischke (the former of whom won the Nobel Prize last year for these findings) or Causal Inference: The Mixtape. Our capability of being very confident about causality in data is definitely limited to when we can find these “natural experiments,” but researchers have been able to find quite a lot and it really forms the basis of modern empirical economics research.