Encounter With The Unknown

Izuku Midoriya was quirkless until he received One For All.
Or so they thought...

While out at the mall with friends, Izuku is caught off-guard and killed by Shigaraki. While everyone mourns for his death, Izuku is reborn using his unknown quirk. Without any memory of his previous life, Izuku begins to live a new life as Haru Tsuki.

Years pass, and Izuku is discovered by All Might, who never really moved on...