Based on rough estimates that assume the minimal required time for all tasks, it is possible to fit all of the above into the 7 years after graduating high school at ~18 years old... if he takes 4 years to graduate from Starfleet Academy and then 3 years for everything else. However, it seems awfully young when you consider everything that needed to happen:
- Graduation from Starfleet Academy (4 years).
- Service on the USS Exeter, probably long enough to be promoted to Lieutenant Junior Grade (based on Janeway field-promoting him to this rank instead of Ensign).
- The incident that killed three officers which would require investigation, information gathering, questioning, arraignment, and motions in the case of a misdemeanor. If the plea isn't accepted or if they choose to prosecute as a felony, there's the additional trial(s), judgement, and sentencing.
- He starts heavily drinking (heavily enough that Chakotay knew about it and accused Tom of being a mercenary willing to fight for anyone who paid his bar bills) and "looking for fights", and he eventually ends up in the Demilitarized Zone.
- Finding and eventually working for the Maquis (which we know was short-lived).
- His capture and arrest by the Federation that was likely under the charge of treason or terrorism, requiring another investigation, information gathering, arraignment, motions, trial(s), judgement, and sentencing.
- The initial time served in his 18 month sentence in the penal colony before Janeway recruits him.
- Not to mention the travel time: to/from the USS Exeter, to/around the Demilitarized Zone, to/from Earth, etc.
On the official Star Trek website, I noticed what appears to be a log entry made by the Doctor during the events of VOY:"Threshold":
In the euphoria of the moment before his first test flight, Paris remarked that it was the first time in 10 years (or since 2362) that he felt his self-esteem was capable of taking risks; I am unsure to what life event he is referring.
Of course this reflects Tom's words in the episode:
Captain, this is the first time in 10 years I feel I have a life to risk.
Which he says after explaining that everyone used to think he'd do something important when he grows up but that "obviously that didn't happen".
We (the audience) don't know which life event that Tom is referring to either. If Tom were indeed 25 years old in Season 1 (making him 26 when the Doctor recorded that log entry), then the "life event" would be sometime in high school at ~16 years of age. That's possible but, in my opinion, unlikely. It seems more likely that he's referring to the incident that killed the three officers. He could have been as young as ~22 years old when that happened, making him 32 in Season 2 of VOY, which corresponds correctly to the actual age of the actor, Robert Duncan McNeill, at the time.
So, what is the supporting evidence for Memory Beta's claim that he is born in 2346?
I've just revisited Tom's Memory Alpha page this has been added:
While Tom's age was never revealed in the series, to establish a date of birth, it was established in "The Killing Game" and "The Killing Game, Part II" that his holographic alter ego, Bobby Davis, was 26 years old. If this was any indication of his true age in 2373, then Tom may have been born around 2347.
That would make him 24-25 in Season 1 of VOY (depending on his birthdate). However, is there any evidence that the biographical data of Bobby Davis is related to Tom's biographical data? Did the Hirogen only tweak parts of Tom's memory, or did they give him the entire profile of Bobby Davis (including Bobby's age)? The latter seems more likely.
Are there other episodes that may support this interesting addition to the question?