Decision at Midnight
The first adventure of the crew of the U.S.S. Larson actually begins before the crew has been introduced to the ship.
The crew, most of them newly minted Lieutenants, are assigned to the U.S.S. Arkadelphia, as seen in the classic FASA adventure "Decision at Midnight".
I tweaked the adventure some to make it better fit the campaign, but first a synopsis for those unfamiliar with the adventure.
Decision at Midnight Synopsis
The U.S.S. Arkadelphia is patrolling the border of the "Asparax Confederation", a breakaway region of space (with 4 planets) on the Federation-Klingon border. The ship's captain is convinced that the Klingons will exploit the situation as they did Axanar, an incident which began the Four Years War between the Federation and the Klingons.
Along the way the Captain begins showing signs of mental instability, starting with eccentricities like wearing ceremonial robes, all the way to full blown paranoia. The players are thus forced to decide whether to mutiny against the captain and how, in keeping with their oaths as Star Fleet officers.
In our version of the adventure, the Captain is actually a Mirror Universe Infiltrator and has a secret agenda: Asparaxian Space actually is an area of "weak space" between the prime universe and the Mirror Universe. His "instability" is just his naturally paranoid personality coming through.
Also aboard the ship is crewman Rogers, an agent of Section 31 who knows the truth about the captain and has a piece of advanced tech that will prove the captain is from another universe. Early in the adventure he takes the PCs into his confidence. At first they think he's insane but gradually come around as the captain gets more and more unstable.
Once the Captain's madness becomes impossible to ignore, with Klingon warships en route, the PCs made their move to remove the captain but not before he could activate the deflector dish and open a rift between the prime and Mirror universes.
As the PCs remove the captain from power a ship streaks by through the rift: the U.S.S. Defiant, thought lost in action with the Tholians but actually transported to the Mirror Universe. The old Constitution-style cruiser streaked past the Arkadelphia, in the throes of mutiny, filled with refugees from the Mirror Universe.