Learning causality from observational data is hard, but there are statistical methods to help with that. Of course, you want to verify statistical findings with experiments, but first you want to find most likely causal relations from large number of correlations.
Causal direction between the two variables can sometimes be identified by observation because there is more information in the data than correlation coefficient and it can be asymmetrical.
Here is nice intro:
Causal discovery and inference: concepts and recent methodological advances
Peter Spirtes and Kun Zhang
Nice paper and method:
Distinguishing Causes from Effects using
Nonlinear Acyclic Causal Models