Izuku actually trained himself physically before having met All Might, and was able to get Bakugou away from the Sludge Villain, and once that had happened, All Might stepped in and finished off the Villain. Izuku still gets reprimanded, but snaps back at the heroes, seeing as he did their job, then leaves while they're all stunned. On his way home, Bakugou still does his whole thing, and then storms off before Izuku could respond. Before he can meet All Might though, he gets Isekai'd to the world of One Piece.
Side note, UA is a University, like in most of my fics, but the Sludge Villain Incident still happens during their last years of Junior High. I'm doing this so I don't have to put a time dilation factor into this story. I'm still gonna l, but that's not the point. The dilation factor is 3 years in MHA is 5 years in One Piece. I'll decide later if I want him in 1-A, or if I want him in 3-A. Either way, this should be fun!
Transmigrated into DxD World-Kuoh Town, Hibari Kyoya. an average student, spent 18 agonizing years in the world fully aware of the dangers, knowing he is utterly powerless in a world of gods and monsters, Until...
[Ding! Sign-In System loading... 20%... 50%... 80%... 100%.]
Destiny, it seems.. has a cruel sense of humor. A [Sign-In System], long overdue, finally bursts to life within him, offering a chance at survival, a chance at power...
[Ding! Congratulations! You have received the Rainbow-Grade Gift Bag!]
...
He then started completing System's tasks, accumulating even greater rewards.
[Ding! Task completed. Reward: Perfect Rumble-Rumble Fruit (Weakness to water Removed).]
[Ding! Task completed. Congratulations to the host for obtaining the Flying Thunder God Technique!]