It's true that cut scenes help steer the player in the direction the story is going, and having them go in a linear order is crucial to how well the story unfolds.
There's also other storylines in space than just aliens. Here's a few that might help:
1.) (Asteroid/comet/rogue planet) headed to earth.
2.) Earths gravity shifting to where it:
a.) Tears earth into pieces that are drifting apart.
b.) Sends people into space due to lack of gravity or reversed gravity.
Affecting the hero/crew of the ship:
1.) There's an oxygen leak.
2.) There's a strange illness.
3.) There's a mysterious passenger.
4.) The ship has ran out of fuel, or the ship is damaged.
5.) The ship's mass is to great that unless they unload some cargo, they will all crash into a planet or won't be able to leave a planet.
6.) A crew member must sacrifice themself in order for the rest to achieve their goal (i.e. we only have enough food or oxygen for 4 people to return home).
1.) Newly discovered alien device that:
a.) Does something amazing like turning kittylitter into gold.
b.) Comes with the terrible cost of removing a year from your lifespan.
c.) Causes you to become some threat to the aliens that created it.
2.) New technology that enables humans:
a.) Travel to anywhere in the universe.
b.) But ravages the planet every time it's used.
Using these in combination you could get something like:
A newly discovered techology allows a crew of 10 to travel to a distant alien planet where they discover a device that will turn kittylitter to gold. The use of this technology came with a devestating cost of shifting the earths gravity and thus tearing the earth into giant floating pieces that are slowly drifting apart. Upon returning the ship was badly damaged and few crew members were sacrificed so the remaining crew could re-enter the fractured worlds atmosphere and turn the worlds kitty-litter into gold thus funding a device that would save humanity (because nothing is free apparently).
Just a rediculous suggestion that hopefully gives you some ideas on how to formulate a story