This story, like many before, starts with a number one hero and his fan on a rooftop.
"Can a person with a quirk so useless they're essentially quirkless be a hero?"
And the number one hero doesn't answer in a way that satisfies the fan, just sputters blood and shows his wounds.
"It's important to have realistic goals, kid. Tell no one about this." And with that he turns to leave.
"Oh. Right. Then wouldn't you mind telling me what One For All is?" The fan asks.
The number one hero coughs up blood again and turns sharply. He finds no malice in the fan's expression, only curiosity.
"Who told you that name?"
"My quirk. It says it's a part of your skillset."
The number one hero stands in silence.
"Maybe," he eventually says, "Your quirk is less useless than you think it is." And with that he leaves.
Smoke covers the sky and the fan makes his way down the stairs faster than the hero, pushing himself through in front of him, taking two steps at a time. (The hero is baffled by such behaviour.) He arrives at the scene, takes it in, breathes in the smoke and lunges forward. His quirk tells him to keep the distance, not throw himself into danger, so he doesn't, but he takes out a book out of his backpack ignoring the calls of distressed people around him and throws it at the sludge villain's eyes, then another, then another, until he runs out of ammunition and the villain, seething, lunges at him. Except somehow his legs move before fear can freeze them, and he does a backflip, kicking the villain into the eyes again.
There was a change, sometime between him getting attacked by the sludge villain and waking up to All Might's voice. The hero must have touched him somewhere, probably slapping him on the face to wake him up if the sting is anything to go by. Because he now knows things he didn't before, he now feels things he wasn't aware of before, he now can do things he wasn't sure his body could handle before.
He can fight now.
So he does, moving back all the while, kicking and punching wherever he sees the sludge villain's solid parts. (There's quite a few. The sludge is just a barrier, it appears.) And then suddenly he is grabbed from behind, gently, and moved to stand behind a broad back, and then Kacchan is grabbed through the sludge, and the villain is blown away with a punch so strong the clouds overhead start crying.
"Shounen," All Might says before either Kacchan or other heroes can get a word in. "That was incredibly brave what you just did."
"Couldn't have done it without your skills," Izuku says, hacks some sludge that was left in his lungs from before, and promptly passes out.