https://m.youtube.com/watch?v=N4nwMDZYXTI
For context, Gibson injured both legs (left hamstring and right knee) during the playoffs and it was unclear if he could even hit the ball. He wasn’t even planning on playing that day and was doing physical therapy during the game with the broadcast on in the background. Vin Scully (the commentator) remarked that he was “nowhere to be found” and that motivated him to suit up and tell the manager he was available to pinch hit.
You can see during his at bat how weak his legs are — his legs shake visibly and he stumbles after his swings. Moreover, he’s facing a future hall of fame pitcher. Nobody expected he’d be able to hit a home run, the manager was just hoping he’d hit a long single to tie the game. However, Gibson knew, thanks to the coaching staff, that the pitcher had a favorite pitch when the count was 3-2 and he crushed the hell out of it.
https://www.youtube.com/watch?v=T8HCF2cef74
(The wave at 2:46)
Surfer magazine ran it on the cover that month with the caption "Oh my God ..." https://northshorehawaii.wordpress.com/laird-hamilton/
The surfing world was forever changed.
I don't know if it's the best sporting moment of all time, but it's certainly an interesting one.
The more accurate answer is probably something akin to Jackie Robinson but that was before my time.