Actually, I'm not sure that going to warp produces that many gees, if any at all.
From Memory Alpha:
A starship could not jump to warp speed without inertial dampers, as the rapid acceleration would smash the crew into the walls, killing them instantly. (VOY: "Tattoo")
Interesting, but I wonder if that means that they would get smashed into the walls if they aren't strapped in like Cochrane, Riker, and LaForge were in the Phoenix (which seems to be a something that ships lack in the Star Trek Universe most of the time), or that it would still produce more gees than the body can handle, killing them regardless (explaining the lack of safety harnesses: it would only keep the bodies from smashing up against something, but the g-forces would still be fatal. Then again, maybe I should brush up on my knowledge of how many gees the human body can take before it becomes impossible to function, e.i., you pass out, and when the acceleration just becomes outright fatal).
If it is the latter, then that means that the inertial dampener must've been invented no later than 2063.