Sven Ottke and Jess Willard were both 29, when they made their pro debut... with Ottke being the oldest at 29Y, 9M, 19D. Willard was 29Y, 1M, 17d when he turned pro... and I don't think, he had any previous amateur experience.
It would also depend on what source your going by. Johnny Buff started his career in January of 1919 and Ring Record Book has him being born on June 12, 1888, which would make him 30, but BoxRec has his birth at Novermber 26, 1891. Wikipedia and Cyder Boxing Zone also have him being born on June 12, 1888.
Bonecrusher Smith is just behind Jess Willard, at 29. Had DaVarryl Williamson beaten Chris Byrd, he would have become champion despite not turning pro until age 31.
If you're counting entering the sport as opposed to simply debuting as a pro, Sergio Martinez didn't enter a boxing gym until he was 20 years old.
Luis "Lumumba" Estaba made his professional debut at age 29 plus six months and two weeks. (Born 8-13-1967, debuted 2-18-1967.) Lumumba won the WBA LFW Title at age 37. An active champion, he was the first world light flyweight champion to reach ten successful title defenses, finally losing it in his 12th defense to Freddie Castillo at age 39. (He needed to be active because Venezuelan law mandated retirement at age 40.) Ottke had over 300 amateur bouts and was a veteran of three Olympiads. I've been able to find a record of Lumumba defeating 1968 Gold Medalist Franciso Rodriguez in the 1964 national amateur championships, but haven't delved more deeply into his amateur background.
what i meant was somebody who never boxed in their life then suddenly at the spur of the moment decided to take it up and was good enopugh to win a title at an advanced age.