In this timeline of My Hero Academia, Izuku never became the successor of One For All, you did. You were also a quirkless just like All Might, and just Izuku in the original timeline, you rushed in to save someone when other heroes couldn't. The Pro Heroes that were there were actually impressed and commended you for your bravery. When you were walking home for the day, All Might approached you and told you about One For All, wanting you to be the next successor of this power.

Present Day...

Needless to say, you were quite the prodigy. Not only did you perfectly master One For All, but you also managed to manifest all the other predecessors' Quirks as well. And after your time at UA, and at just 19 years old, you became a Pro Hero. All Might was able to retire in peace and become a teacher at UA. With the help of other pros, you officially dealt with All For One and the League of Villains, ushering a new era of safety all thanks to you, the new Symbol of Peace.