Einstein won his Nobel Prize for explaining the photoelectric effect, a measured phenomenon that didn't have an adequate explanation.

His work on brownian motion showed that the observations of the movements of small particles can be explained by the nature of fluids as being made up of small particles (i.e. molecules).

Special relativity is what you get when you combine the seemingly contradictory observed phenomena that there's no such thing as absolute motion and that the speed of light is a constant to all observers.

General relativity combines that with the observed phenomenon of gravity.

While I don't know whether these constitute "proof," Einstein certainly had a lot of empirical support for his ideas, and they weren't anything like pure intuition.

Why do you think this addresses the claim "Reasoning from intuition has a terrible track record?"

1) Einstein didn't work from intuition, but from a particularly narrow insistence on that the laws of physics be the same for all observers. This informed both SR and GR, and in fact his "intuition", such as it was, led him wildly astray in the run-up to GR. His papers in the 1913-1915 timeframe were all over the map. Furthermore, the final decades of Einstein's life were almost completely sterile in terms of new physics because he let his intuition guide him: he insisted that "god does not play dice" and so on, which turned out to be a hiding to nowhere.

2) Even if Einstein had worked primarily on the basis of intuition (which he didn't) and had been right (which he wasn't when he relied primarily on intuition) it would not in any way absolve us from the duty of taking experimental results far more seriously than theoretical intuitions, because against that one (actually imaginary) triumph of intuition we would have to balance thousands of years of intuitions from very smart people that turned out to be false.

"Things fall toward the center of the Earth and planets move in perfect circles about it" was intuitively obvious to Aristotle. So were a lot of other falsehoods. Galen had a whole raft of intuitions about human physiology that were false. Everyone from Kant to the Positivists believed it was intuitively obvious that detecting a violation of the law of non-contradiction of the kind implied by the experimental violation of Bell's inequalities was impossible. And so on.

So even if we had a single instance of intuition being correct, we would still be crazy to rely on it given its long track record of abject failure. "It just makes sense" are the most dangerous four words you can speak, because they are the terminus of critical thought.

For special relativity, yes. (Maxwell's equations plus the negative result of the Michaelson-Morley experiment.)

Einstein started with large amounts of empirical data and created models that explained them.

Special relativity still holds where it is applicable, and general relativity has yet to be refuted, and has been verified in interesting ways (gravitational lensing of Mercury with regards to the precession of it's perihelion for example). Einstein's other ideas about phenomenon such as the photoelectric effect and Brownian motion have been long since verified, so I would say, especially in comparison to some of his contemporaries, his theories oh withstood the test of time very well.

Part of Einstein's genius was that he took seriously the fact that in all the empirical data, no one had yet found a way to distinguish between inertial acceleration and gravitational acceleration. He decided this was not a coincidence, but a fundamental equivalence. It resulted in his elevator thought experiment that predicted that gravity can bend light.