There are two answers here:

(1) In one sense, we can infer causal relations from observations. There is quite a large literature on both estimating causal effects from observational data, and on learning causal structure from data. However, for both of these problems you need quite strong assumptions (causal assumptions) that make the game work. You cannot create causality from nothing.

(1a) It is also not quite true that we always need to use observations to infer causality. If you look at a little kid exploring the world, (s)he will always be pushing/prodding things in the environment -- experimenting to discover causal relations. I went to a talk (http://www.alisongopnik.com/) that showed a video of kids aged about 5 figuring out a causal arrow in a little Newtonian gear system by doing experiments. Humans are very good at getting causality from experimental data, even while young!

(2) In another sense, causality is a "useful fiction" like the derivative or real numbers. If you look at the Universe on the scale of the universal wave function, there is no causality, just the evolution equation. But if we look at the scale of "individual agents", it is a useful abstraction to talk about arbitrary interventions, which is a building block from which certain kinds of notions of "causality" spring from.