Not really. Pretty sure I read recently that Newton appreciated that his theory was non-local and didn't like what Einstein later called "spooky action at a distance". The Lorentz transform was also known from 1887. Time dilation was understood from 1900. Poincaré figured out in 1905 that it was a mathematical group. Einstein put a bow on it all by figuring out that you could derive it from the principle of relativity and keeping the speed of light constant in all inertial reference frames.

I'm not sure about GR, but I know that it is built on the foundations of differential geometry, which Einstein definitely didn't invent (I think that's the source of his "I assure you whatever your difficulties in mathematics are, that mine are much greater" quote because he was struggling to understand Hilbert's math).

And really Cauchy, Hilbert, and those kinds of mathematicians I'd put above Einstein in building entirely new worlds of mathematics...

Agree with you everywhere. Although I prefer the quote:

"Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore."

:)