Is this Saiyan scenario? :)
As for the answer, the same way evolutionary pressures work anyway. Lets say there was a mutation allowing you to use some invisible power or magical energy. It would allow those possessing the mutation to survive where others do not. Those mutated genes spread slightly better than the alternative, but noticeably.
Then, disaster strikes and the only survivors are those carrying mutated genes. And the funny thing is, similar scenario already happened. Long ago, in a distant past, there was no oxygen in the atmosphere. Suddenly, cyanobacteria, those multiplying masters of green, invented photosynthesis. It produced pure oxygen as a biproduct. And oxygen was a poison to all competitors of the bacteria. Only those who got immunity somehow or found how to survive with poison all around them got to live and procreate. More details https://en.wikipedia.org/wiki/Great_Oxygenation_Event
Fight or flight response, extremely hightened? Your body is stronger than you know, there are artificial limits preventing you from regularly punching doors off a car and lifting trucks that fell on your child. Basically, you can do that, but you can't do that all the time, because your body will tear itself apart. Your arm muscles are strong enough to break your arm; maybe those with mutation are able to sort of remove those limits one at a time or get hightened perception of their own real strength. Basically, we are all Shaolin monks in dangerous situations, only in 5 seconds bursts.
See here: https://abcnews.go.com/blogs/headlines/2013/04/teen-daughters-lift-3000-pound-tractor-off-dad/