(The motivation for the below question is to explain the concept of the so-called scientific evidence to laymen.)
(I am sorry that the question is somewhat broad.)
What would be a fitting (and preferably with an interesting story) for:
An eventual physical discovery that was hypothesized before the discovery itself (due to prior knowledge or data collected from observations); and before devising the experiments, the scientists determined what would be an evidence to support the hypothesis.
(One example I can think of is the discovery of the Higgs boson. It was predicted by the standard model. The scientists had some idea about where to look for it, and what would constitute as an evidence, and finally they discovered it.)
I would prefer cases that can be explained to a layman in simple terms, and where I can reach to sources where I can learn the whole story in non-technical terms.