No, experiments showing a fixed speed of light came first. Ex: 1887 https://en.wikipedia.org/wiki/Michelson–Morley_experiment It’s a critical point people miss. Rather than come up with his ideas in a vacuum Albert Einstein instead was trying to explain some results which seemed really counterintuitive.

He made many other predictions which where tested afterwards. People also repeated the speed of lights tests in new ways, but the light experiments where consistent with earlier results.