I'm bad at "pilots" AKA origin stories so we're gonna speedrun this.
Izuku's history is the same,he's bullied and told to delete himself,he walks through the shortcut area,but this is when things change.
In the area he finds a canister filled with a black substance. This is when the sludge villain gets him and makes Izuku drop said canister.The lid gets a little loose as the symbiote gets out and latches onto Izuku.Black tendrils spike out from him and push the villain away,a suit doesn't form yet.
All might comes and "saves the day" Izuku grabs on to all might.They have the same conversation.Izuku finds Bakugo being taken by the villain and tries to save him.Here's where things change again.
When charging at the villain,a black substance covers his legs and soon,his whole body.
Izuku feels faster but assumes it's adrenaline and proceeds to Bakugo,this time,when pulling at the sludge,he actually peels it away and saves Bakugo.
Bakugo:What the hell Deku!?What are you wearing?!
Deku;What do you mean?This is just my school uniform.
But next to Izuku is a glass building,as he sees his reflection,he freaks himself out and isn't sure what happened.
The sludge villain charges at Izuku,but before he gets to him,all might,who was motivated and inspired by Izuku's bravery,saves the day again.When all is said and done and everyone goes home,Bakugo says nothing to Izuku.All might makes his appearance still though.
All might:Young man,I want to thank you,thanks to what you did that boy is safe.I would like to help you master your newfound power,if you'd let me.Because let me tell you something boy,YOU CAN BE A HERO!
Izuku,while happy at the notion,declined the offer,much to the hero's surprise.
Izuku:I'm sorry sir,but I'd like to find this out on my own.
All might respected his wishes but still told him about the beach,suggesting it as a training ground for him.Izuku decided on it being his training ground and went home,happy that now he has a quirk.But little did he know,he didn't just get a new power,he got a new friend.