So, AU in which Hagrid didn’t get framed for murder and expelled. We’ll say Aragog never happened and Tom settled on a different fall guy. Myrtle dies and Riddle gets away with it, but Rubeus is not a casualty of the plot.
His written coursework was never going to be great, even if he hadn’t been orphaned at age twelve, but his practical casting gets more noticeably excellent, the more the spells they’re learning benefit from having more power behind them.
Dumbledore made a teacher’s pet of him from the beginning, because he wants to see the half-giant kid Dippet almost didn’t let in succeed, so he’s always worked hardest in Transfiguration. Once Albus notices there’s actual potential here, he keeps assigning him different tutors trying to find someone who can get transfiguration theory into his head because once this kid figures out what the hell he’s doing he’s really good. He starts taking all the kid’s detentions and assigning them as tutoring sessions.
Toward the end of fourth year he tries Minnie McGonagall, a prefect who is ironically in detention for cursing a Slytherin prefect during an argument about politics.
Rubeus gets five OWLs and the Transfiguration score is actually pretty high. The next year, he turns out to be a natural at nonverbal casting. His DADA scores climb steadily.
The summer before Rubeus’ seventh year, his Transfiguration Professor goes to Europe and defeats a Dark Lord. When he comes back, everyone is incredibly excited to have the Conqueror of Grindelwald among them and keeps praising him and thanking him and telling him how proud they are and how proud he must be to be such a hero.
Rubeus is the only one who seems to notice that his favorite teacher seems really, really sad. He bakes him an inedible cake. Albus finds himself smiling and meaning it for the first time in at least three months after he nearly breaks a tooth on it.
Where has one of his favorite students been spending the summers since second year, anyway? Do wizards have their own orphanages? Did Hagrid’s father have relatives that put him up?
(It’s 1946, there aren’t a lot of government regulations covering this kind of thing even for Muggles yet, and the situation of ‘homeless orphan who spends nine months a year at boarding school’ is unprecedented in my experience because those usually cost money.)
Rubeus gets three NEWTs: Transfiguration, DADA, and (with flying colors) Care of Magical Creatures. He gets a job with the winged-horse breeders. Offends the young Abraxas Malfoy by being Entirely Too Large and Not Human and In his Stables. Gets fired. He gets a job at the Welsh Green reserve out west. Gets attached to a particular elderly dragon scheduled for slaughter. Gets fired.
Manages a position at the Department for the Regulation and Control of Magical Creatures–a real grunt position, not at all what you’d expect for someone with such high NEWTs and glowing letters of recommendation from his teachers, even if he has been fired twice, but that’s institutional prejudice for you. Mostly they have him deal with dangerous animals, which is just how he likes it.
Manages to go several years without being fired, mostly because he’s managed to keep his head down and avoid anybody noticing how many animals he was supposed to kill he actually smuggled home to his house. Complains at length to his old teacher and recently appointed Supreme Mugwump about the rampant unfairness toward splendid beasts and nonhuman persons he sees every day on the job, when Albus drops by with cake to have tea and double-check the wards Hagrid’s cast to keep any of his rescues from getting out of the woods around his house.
Is eventually fired, but not for the creature-hoarding because that would probably get him jail time.
Now-Headmaster Dumbledore convinces Professor Kettleburn, who has just lost an arm, that an Adjunct Professor who’s practically indestructible would be just the thing.
By 1970 Rubeus Hagrid is the main CMC Professor and Kettleburn does periodic safety lectures (directed mostly toward Hagrid with the kids learning sort of incidentally; it actually stick with them better that way) and some of the advanced theory topics, and spends the rest of his time doing research in the Forbidden Forest. (Binns is now also a Professor Emeritus and delivers most of his lectures to rooms full of marble busts. He doesn’t seem to have noticed.)
Lily Evans is one of his favorite students. Remus Lupin is teacher’s pet.
Rubeus Hagrid, fully accredited wizard who can shrug off stunners even without any kind of armor, is a battle tank of the Order of the Phoenix. He and Moody take down enough Death Eaters together to have Voldemort wishing he’d killed that ugly half-giant kid when they were in school, instead of the useless Ravenclaw girl.