at the age of 4 izuku midoriya was told he has a weak quirk that would just make it where he can evolve when he gets injured but the effect is very small and the quirk gives him a small healing factor. 

after hearing this izuku was happy but also disappointed that he did not have a flashy quirk like all might, but when he went to his preschool he was greeted with disappointed and unforgiving children, he was mocked and bullied for having such a weak quirk. but eventually, he would get sick of this and tell his parents, (he was 5 at the time) but to his shock and horror, they did not care they would just tell him to get into the car izuku listened to what they said later he regretted this.

after they stopped izuku was pulled out of the car and pushed into the forest and he was left there with just the clothes on his back.

izuku thought that they would come back so he waited and waited but they did not come back and on the 4th day izuku gave up hope of them coming back for him,

he then wonders to the nearest settlement meant which was quite far for anyone but thanks to his quirk he did not have to rest as much as a normal child or person because he was chased a lot he had quite a large supply of stamina but it was no were near what some quirks give there user's.

so it only took him 4 days instead of the 10 days it would take a normal person on foot but people with a quirk that even gave them a small boost would have made the trip in 1 day at the same age.

when he got there he was not treated with what he usually saw In a town there were buildings that were about to crumble and people on the streets begging but the people in funny uniforms would not give them a second glance, then one of the people in funny uniforms came over to him and asked what he was doing here and izuku told him what happened because he was afraid and scared and during the explanation, he told the man his quirk and the man then dragged him to a building and inside there was a man that stood at 6 foot 5 inches he had a scare on his face that looked like his eye was gouged out but he still had both his eyes he was very intimidating to the boy. 

when he spoke he scared the boy with the venom in the man's voice " why have you brought a child to me, gipo" 

the now sweating gipo hurried said " captain this child has a quirk that could help us get revenge" 

the captain then asks in a voice that showed his interest " what is the boy's quirk " 

gipo now a lot less scared said " the boy has a sort of evolution quirk"

the captain was very interested now " how does it work "

gipo told izuku to tell the man how his quirk worked

izuku shakily told the man that his quirk was very weak but he could evolve in a way.

the captain cut him off with a terrifying smile and said to gipo that he should get the boy ready to serve in their ranks.