My guess is that he's in his early thirties.
Advanced degree from MIT mean's he was at least 26 when he graduated, and no secret government research facility is going to hire a freshly minted PhD. He probably got 5+ years of experience, then got hired on at Black Mesa, possibly as a post doc. It's more likely the other scientists were too old or to self important to do what could be considered seriously hazardous work.
It's pretty obvious that he was put into stasis at the end of Half Life, as evidenced by the fact that they explicitly said so, and everyone says that he doesn't look like he's changed at all. Thusly, he's physically the same age as he was at the end of Half Life, i.e early to mid thirties, but if you look at his birth certificate, it says he's in his forties.
EDIT: Forget all that, the game explictly say's he's 27 at the events, so he's 27 in H2.