The main character is a child. He enrolls in a school that has commoners or whatnot and he hides his power from his classmates. They think he is a commoner and treat him like trash. One day, they explore and meet a big goblin or whatever, and he tries to protect one of their classmates, and he falls, and everyone thinks he died, but he didn't.
This is likely Seirei Gensouki: Spirit Chronicles
Meet Rio: a callous orphaned boy living in the slums. At only 7-years-old, he realizes he’s actually the reincarnation of Haruto Amakawa, a Japanese university student with a tragic past. While still reeling from this shocking epiphany, Rio also comes to learn that he possesses extremely potent magical abilities and uses his new powers to solve the kidnapping case of a little girl. His good deed is acknowledged, and he’s rewarded by being enrolled into… a prestigious academy for noble children...?
The main character enrolls in the noble academy, and is treated like trash on account of being an orphan and/or commoner.
The scene with the goblins and the orc is chapter 10; during an excursion his classmates meet some goblins which they can easily take care of, and a giant orc, which they can't. A female classmate is pushed off a cliff; he jumps to save her. Due to his hidden powers he's able to survive, but they assume that he's dead, and also that he's the one that pushed her off in the first place.