Well, I think we can get a minimum age for CJ.
The game is set in 1992, just as CJ returns from Liberty City after living there for five years. So he originally left San Andreas for Liberty City in 1987. Since one has to be at least 18 years old in America to travel and live alone, we can figure out that CJ must have been born as late as 1969, making him at least 23 years old during the events of the game.
However, let's assume I'm not realising there's a way to travel and live alone under the age of 18.
CJ can purchase alcohol while on dates. I'm going to assume he does so legally. Los Santos is a parody of the real-life Los Angeles. I couldn't find a source that explicitly states the legal drinking age in San Francisco in 1992, so I'm going to assume it's 21, which is the most common legal drinking age in the United States. So, assuming CJ did travel to Liberty City under the age of 18, that means he must be at least 21 years old as of 1992, meaning he was born in 1971 at the very latest.