We have observations that match quite well what would be expected if there was additional matter in the universe. We cannot detect this matter though, so the conjecture is that there must be something that interacts gravitationally with the rest of the universe but not in other ways. We call it dark matter for now. We do not yet know what it consists of, there are even competing theories but mapping the effects of it? That we can do.
This approach is not at all unusual. If you want to know about another example from a different field, look no further than genetics.
Gregor Mendel observed rules for inheritance of certain traits in plants and was able to make predictions from that. He discovered genetics. In the 1850-60ies. This was a long time before Crick, Watson and Franklin discovered the structure of the underlying mechanism for inheritance (DNA).