From a rough estimation POV
If Tom was born in 2346
The accident in which Paris covered up was during his first assignment, onboard the USS Exeter, if we say Paris entered the Academy at 18 and graduated 4 years later at 22, then we can put the time of this accident sometime after, say a year later (2369)
Later he joins the Maquis and is captured by the Federation a few weeks after, he is imprisoned on the Penal Colony, for maybe two and a half years (considering his parole was upcoming when Janeway met him), he later accepts the mission for Voyager (2371)
So if we go by this method, Tom is 25 years old when he first boards Voyager