I think that historically both patterns exist, and they correspond exactly to two modes of human thinking. One is to obtain theory through sensory experience, and the other is to arrive at theory through reason and then test it through experience. It is through this repeated process of exploration that human civilization continues to progress. Of course, both depend on experiment, and both are ways of obtaining a posteriori knowledge. There is also another kind of knowledge that exists in advance and makes experience possible. This can roughly be called a priori knowledge. This topic is mentioned in Kant's Critique of Pure Reason.

Both paths exist, and science needs both.

The second one more often, but both happen. Many times, a phenomenon accidentally observed in an experiment inspires scientists to come up with a new idea. But there are also many cases where scientists first propose an idea and then design experiments to test it. There is no fixed order in scientific research; observation and thinking push each other forward and together lead to scientific discovery.

Among famous cases, apart from general relativity, all started from experiments; only general relativity was partly built theory-first. In this respect, general and special relativity are very far apart—not as their names might suggest.

Experiment first, then theory.

I would say both cases exist. Scientists usually might start from an overall theory that may not be perfect, but they have an expected result in mind. With this in mind, they conduct experiments to get good findings. The opposite is also applicable. Scientists may accidentally come upon a logical chain that can form a theory to explain an observation during an experiment, perhaps for fun or for other purposes. Note that “experiment” is not restricted to the lab.

The second one usually comes first, but not necessarily an experiment—rather, typically an observation. Karl Popper once stated, “the criterion of the scientific status of a theory is its falsifiability, or refutability, or testability.” If a theory matches every possible observation but makes no testable predictions, the theory is meaningless. However, it is worth noting that every theory should have a certain observational basis. Hence, a good theory should always have ideas that scientists want to test, which usually stem from observations of reality.

Either can come first: ideas guide experiments, and unexpected results inspire new ideas. However, scientists’ assumptions influence what they test and how they interpret it.