It starts earlier than puberty. In my area, flag goes through 2nd grade. Third grade is the first year of tackle (though many second graders play up). 2nd grade, this other team has a little kid who is quicker than anyone on the field. His dad was the coach. They would run a play on first, second, and third down giving three different kids a chance to run a play, or run the ball. We'd stop them. Then on 4th down, he just ran a QB keeper, and he ran for a touchdown....every....single....time. We literally could not touch the kid he was so fast.
Fast forward a year to third grade. The family moved so now we are playing against them in tackle. The kid is still the fastest by far, but at least we have more kids on the field, so we can get close to him. No problem for him though because he delivers a devastating stiff arm to the forehead of anyone who gets within arms reach. I pleaded my case to the refs that our league outlawed stiff arms to the helmet by ball carriers after a kid was sent to the hospital with a back injury after a ball carrier grabed his facemask and rode him to the ground. Both the refs, and opposing coach laughed at my pansiness in thinking a ball carrier can't protect himself with a stiff arm.
Again, this kid wasn't the biggest, strongest or tallest. He was just a very naturally athletic kid gifted with more strenght and speed than most kids his age.
These are not rare exceptions. Every neighborhood, team, school, whatever has that one kid that is above the curve. I see it all the time. I grew up with these kids, and I see them all the time with my kids teams.