Another lesser known wrinkle along these lines is that if more of Aristarchus of Samos' work on heliocentricity had been developed into a "calculational framework" for planetary motion by a contemporaneous Ptolemy competitor (a la Copernicus in 1543), various relativity ideas might well have started in 270BC instead of 1600 AD.
Aristarchus was already WAY ahead of a few games - making a guess that "absolute rest" was illusory and tiny stars were similar to giant Sol. If not for Archimedes' serious star power, we might not even know of Aristarchus' heliocentric ideas! Relativity ideas of various kinds are short intellectual hops from "the absolute rest of your intuition is illusory".
Aristarchus and his supporters just had to assert The Stars were very distant -- far enough for there to be NO PARALLAX! Various "coincidences" all conspired to suppress Aristarchus' plausibility, like: A) Just HOW DISTANT stars are/local galactic stellar density &| B) poor human VISUAL ACUITY relative to C) Earth ORBIT vs. Sun LUMINOSITY (parallax baseline) & maybe existence of Moon to vent atmo &| D) VERY SLOW (3 millennium) development from near prehistoric glass (1500BC) to grinding lenses for human eyes in the 1300s AD leading to Galileo's telescopes & etc. If ANY of (A)..(D) were about ~10x better (ALL of which are imaginably so), the day that universe changed could've been much earlier. Heck, even if Aristarchus just had a really good spin doctor like a major religion pushing the plausibility of "Sun=A close Star", that might've been enough.
Archimedes almost invented the underlying ideas of integration and limits and all that, too. Close but no cigar, but (had that been in hand) analytic geometry and differential equations are short steps away. I mean, Newton surely noted the equivalence of gravitational and inertial "mass" (charge vs. kinematics) which is the weak principle of equivalence of GR, after all. Like I said - "littered". ;-) There are probably whole books written on the topic (or adjacent topics) of "All the Things Humanity Nearly Figured Out Earlier" that have a more historical bent than the usual "sci-fi tilt".