The Stone Hashira: Izuku

Izuku is quirkless, this is a fact. Izuku isn't normal, that is an opinion. Despite being quirkless, Izuku is stupidly strong. Throughout Izuku's life, he picks up a specific style of breathing that puts him on par with those with quirks. Izuku is transferred from Tartarus to Class 1-A (It's in the backstory(He also isn't in the first few chapters))

OR,

Izuku Midoriya is Gyoemi Himejima. Not as a reincarnation though. UA is a university.