Izuku Accidentally Took The Exam To Become A Teacher At U.A And Passes (Nezu, Being the little shit he is, allows this to happen!)
Apparently a last minute exam for hiring a a teacher at U.A was held on the same day as the U.A Student Entrance Exam.
Izuku got lost and went to the wrong room.
Izuku thought the Student Entrance Exam for U.A was kind of weird but didn't think much of it because it was U.A and all which why he was surprised the acceptance letter that came in the mail came with a video of Nedzu congratulating for becoming the youngest heroics teacher in history.
Apparently Izuku had everything Nedzu and The Hero Commission was looking for in a heroics teacher.
Izuku was confused because he thought he needed a hero license to become a teacher but Nedzu told him he was able to pull some strings so he can teach regardless.
Izuku has to prepare lesson plans and teach Class 1A as he figures out in his own how to use One For All.
He was given a provisional hero license right off the back so he can act without instruction of a hero but he has still had to later take the exam to get his full hero license.
Poor kid.
He will be overworked.
But at least he will be allowed to have his own sleeping bag and nap whenever he gets the chance.
But on the bright side he's happy he's co-workers with All Might.