Being a first-time offender does not change the time calculation. The math is the same regardless of criminal history.
In the federal system and most state systems, inmates serve about 85% of their sentence when good time credit is applied. On a three-year sentence that works out to roughly 30.6 months, or just over two and a half years, assuming he keeps a clean disciplinary record throughout.
That 15% good time credit is granted upfront but it is not guaranteed to stay intact. Incident reports, rule violations, and disciplinary infractions can result in good time being taken away, which pushes the release date closer to the full three years. Inmates who protect their good time by staying out of trouble serve the shorter version. Those who accumulate violations serve longer.
Whether parole is a possibility depends entirely on the jurisdiction and what the sentencing judge put in the commitment order. Some state systems still have parole provisions that can move the timeline earlier than the 85% calculation. The federal system eliminated parole for crimes committed after 1987, so federal inmates serve the full 85% without parole consideration.
If he is in a state system and the commitment order includes a parole provision, his first hearing could come earlier than the 30.6-month mark. An attorney or his case manager can pull that document and confirm whether parole is written into his sentence.
The most important thing he can do from day one is protect his good time. Two and a half years with a clean record is significantly better than three years with violations along the way.