I don't recall anything saying that they went to Academy at the same time, but they were both working on the Warp 2 project in First Flight. That's when Archer met Trip, and so they would have known each other - and been working together - for 8 years or so before Archer actually picked Trip to be his First Officer/Chief Engineer. By that time, Trip would have been the resident expert on and probably a main developer of the first Warp 5 ship.
As for education (although I typically ignore everything expressed in TATV), isn't it possible that Trip received his engineering training through Starfleet, and so did not go to a private four year college? I mean, the warp 2 engine may have been a specialized area being worked on only by Starfleet, so maybe they provided his education.