In TNG's Conspiracy, Captain Tryla Scott was supposedly the youngest Captain in Starfleet history, which was a legendary achievement. Kirk's rapid ascension would absolutely obliterate that record.
To be fair, we don't know Tryla Scott's age, and I always assumed she was in her mid twenties. I make that inference because she seemed younger than Riker, who wasn't offered captaincy until his late 20s.
While it's pretty obvious that Kirk's rapid ascension is definitely the record for quickest captaincy, that's not the same as youngest captain, either. Although highly unlikely, Scott might have made captain at the same age as Kirk, considering that Kirk squandered his college years in the JJVerse and that we don't know Scott's birth year.
In any case, I should think that Scott holds the record for fastest captaincy without cheating
King Daniel wrote:
Everyone's back, it seems. Keenser, Cupcake, Pike - I even spotted Madeline in one of the trailers.