No reincarnation/not knowing the plot.
Born into my hero academia with Apocalypses powers he's was born with not the abilities he gained from the celestial tech (marvel comic version not movie). While being cared for by his babysitter he ends up falling from the balcony and dies while being spotted by bystanders as well as the babysitter who looks over the balcony in shock ends up coming back to life thanks to his immortality/regeneration abilities, due to this incident his story ends up the the news and garners the attention of the government and all for one/dr garaki. Before the government and put agents into keeping an i on a potentially powerful hero/asset he ends up being kidnapped by all for one so he could steal his quirk so he could be healed from his injuries unfortunately for him he is unable to steal his quirk he decides to raise the boy for dr garaki to experiment on the boy to see if they can perfect their nomu even further and to get a potentially powerful ally and all for one to hopefully get a successor to pass his quirk onto if he can't find a way to extend his life and finally get the quirk he's always wanted.
Our mc ends up going to UA high to spy on All might since they heard rumours he'll be attending there to teach and find and observe any useful quirks that his father (aka all for one) can use/ his gramps ( dr garaki) can use in his research. But he also has a ambition to become the number 1 hero not out of some heroic ideals or villainous tendencies to gain more power but so he can use the hero's to put down villains that end up becoming to much of nuisance to his criminal empire and so he can better direct the villains to better and easier targets that have less hero's patrolling and gain more influence in the criminal side of society also what quirk user doesn't dream of being the best, he also wished to attend school to help better develop his abilities because his adoptive father may have many quirks and a good teacher about how to control his powers does not mean he won't find inspiration from somewhere else about how he can use his quirk in a different way.
He dose end up getting all for ones quirk which mutates and instead of stealing quirks from others he's able to generate powers he needs himself and that's how he ends up getting all of Apocalypses abilities. And he does have apocalypses blue skin and red eyes.