This is a timeskip; if you wanted more backstory, then you can use your imagination.
You opened your eyes, grinning and changing into your new outfit. Today would be your first day of fifth grade. Although canon would be starting in 4 years, you weren't that scared.
Katsuki kicked open your door while you pulled off your shirt. "HAA!? Lock the door, you stupid BakAni!" He flushed pink, slamming the door closed. "The old hag made pancakes for us, so you better come down and eat!"
As he stomped off, you giggled. Kat really was the weirdest delinquent-boy ever, wasn't he? You got your school things ready- your hero journal(which had expanded into a three-inch binder that was nearly full after only five years of use), school textbook, pencil bag, A/O pin(Future you's pin), and 5 empty notebooks. You just skipped eating- it was just a waste of time, and you got nutrition from photosynthesis now so you didn't bring your old lunch box anymore.
When you'd finished packing, you did your hair and morning routine- which you could now do in 10 minutes flat- then went downstairs after double-checking your plan for taking down All for One.
"Hey Mitsuki-san! Hello, Izu, Inko-san, Kat." You ate a pancake though it didn't taste like anything, and rushed outside so you could make it to the train in time- though you could teleport, you didn't really want to at the time because it was always kinda trippy. When you arrived at the train station, you just barely made it.
Of course, you weren't going to school, you were going to the only important thing for miles around- the Todoroki household. Today was the day you were befriending Shoto, no matter what it took. You'd already told MItsuki-san about your maturity and genius, so she knew you only went to school as a pastime.
She also knew you had to go to UA to get a cheap hero's license, which was why you weren't skipping everything, so she usually let you do anything you wanted.
When you'd arrived at the home, you knocked on the door, then demanded to see Shoto if Enji didn't want what happened to Touya going public. You were let in, and Shoto was placed in front of you."Hi! I'm /name/ and we're best friends now, okay?"
You hit it off instantly- what wasn't there to like, though? You and Shoto were like Ice and Air- compatible, but not the same. Until Shoto asked the dreaded question. "What's your quirk?" You paled, glancing at Enji. "I don't have one. But no mistake, I've beaten up tons of villains! Since I don't use a quirk, it isn't counted as vigilantism!"
Enji's face went dark. "You're quirkless, so how do you even think you can look in Shoto's direction?" You smirked, looking at him. "Well, if I can't then neither can you. Womanizer. Abusive parent. Cares about publicity more than family. No wonder everyone's scared of you."
You smiled coldly, and Shoto gave you a high-five. "C'mon, Sho, let's go to school." You grabbed his arm and walked out, dragging him with you. He had his stuff, and wasn't talking even as you went on the train to your hometown and you let him sign up as Tosho Anirotte in your school.
Leaning on his shoulder, you walked him to class- the same as Izu's and Kat's. "And why do you think /name/ isn't gonna be here for a little bit, Bakugou?" You opened the door. "Heyo! I was just bringing another traumatized kid into our ranks. This is Tosho. He's got an ice quirk!" You sat him next to you in your now TodoBakuDeku table, as well as you, of course. You told Izu and Kat the specifics- not enough they'd guess who his dad was, but enough that they didn't question him.
You smirked as your teacher passed around papers, just getting to meet you and maybe some light homework for history and math. So easy, and you could do it in your sleep. You opened up your phone and started a brand new class on the psychology of villains specifically.
Hopefully, this'd get you through the year without too much of a brain fart. You'd heard that Nezu would be starting classes that taught advanced forms of math and new formulas you'd only learn there, also English.
You'd been born in London in your past life, so you literally were a mute for the first four years of your life- until you broke the rule that you specifically could only speak one language(Now you could subconsciously translate any language, code, or picture easily).
Now that the language gap was gone, you could do anything you liked. It was pretty nice. "Now, present your papers to your table." You blushed, quickly filling it out like a college student finishing homework during a lecture about being on time. You flipped it around so the others could see, then waited for everyone else to finish- well, you'd chosen geniuses for a reason, they'd all been doing the homework..
Kat went first, introducing himself to Shoto directly because honestly everyone else knew him. "I'm Bakugou Katsuki! I'm gonna be the number one, and my quirk is an explosion." Shoto nodded quietly. Kat's grin instantly let you tell that those two would be quick friends.
Then it was Izuku's turn. "I'm Midoriya Izuku! I also wanna be a hero, like All Might! I'm quirkless, though.." You and Kat assured that he would be a hero- as usual- and he smiled thankfully.
Shoto went next, just saying a few things. "I'm Tosho Anirotte. I hate Endeavor. I have an ice quirk." You gave him a head rub and he smiled thankfully. Well, what can you say, no? Like, Shoto Todoroki is the cutest little person ever- and his scar was there but clearly not as healed.
Kat smacked your shoulder. "Oh! Yes, I'm /name/ Anidoret, and I obviously don't have many aspirations other than expanding my family." You grinned nervously. You'd forgotten that you had to introduce yourself because of a little thing called simping. "I'm also quirkless, but that won't stop me from being the best person I can be!"
A few minutes later, the four of you had become the true best of friends. "Ani, if you had a quirk, what type would you want?" You shrugged. "Probably one that could let me repeat the day if I died." Izuku gasped. "But you'd have to live your last day alive forever!" You shrugged.
"Well, that doesn't really bother me much. I could also get into the business of being drugged so I don't remember it- become the world's best info keeper." You smirked, thinking of the consequences of that quirk- they may be bad, but totally worth it. Of course, you'd never want that quirk or for anyone to, because like, you might start thinking you're just a person without any quirk but also hallucinations.
Izu and Kat both said they wanted All Might's quirk, and Shoto just said he wanted to live a life where he didn't have to be so scared all the time. You nodded resolutely, and the others followed your lead as usual.
Of course, eventually Shoto realized you were probably the loudest and most annoying people in that room, but evidently didn't mind much. You smirked at him, and he just gave a small smile.
He'd learn, though.