Schrondinger's cat was a thought experiment created by Schrondinger to highlight the absurdity of the implications of the EPR paradox highlighted by Einstein, Podulsky and Rosen that quantum mechanics at the time was incomplete (and that superposition existed on a larger scale). So at the time there was a debate about whether this was actually the case.
While at the time there was no empirical data to the theory of large scale superposition beyond that it explained small scale superposition seen in previous empirical results, this would later be proven with many larger empirical trials where larger items were held in superposition. So it was through this that it became accepted into scientific theory.
In short the process is:
- Come up with a theory/model that is logically sound, explains previously empirical results and has testable predictions.
- Test its predictions, the more times it is accurate the more likely that it is correct.
- If it turns out some predictions are incorrect it may still be useful for predicting a smaller set of issues (e.g like newtonian physics)