According to the Star Trek Chronology, Sulu was born in the year 2237.

When did Sulu become captain?

In 2290 Demora Sulu entered the Academy. That same year, Hikaru Sulu was promoted to the rank of captain and was offered the command of the Starship Excelsior (NCC-2000).

How did Sulu get his name?

'” As Takei explained, his character was named after the Sulu Sea off the coast of the Philippines. “[Roddenberry] had a map of Asia pinned on the wall and he was staring at it, trying to get some inspiration for the Asian character,” Takei said. ... And that's how my character came to have the name Sulu.”