When Harry blows up his aunt during the summer, Dumbledore is much quicker to react. Snape finds him far before the Minister does, but his plan of dropping him off with a lecture and half a dozen additional summer assignments doesn't work out. In which Harry spends the summer at Spinner's End.
Izuku has been friendless for most of his life. He's so used to making himself invisible that he fails to befriend a single person in 1-C. By the time he transfers to 1-A, he's just accepted that he'll continue to be on his own for three more miserable years. His new classmates strongly disagree.