Beginnings are tricky. You want to give the reader what they need to know without bogging things down. I'm not sure there's a one-size-fits-all solution, but a couple of tips:
1) Consider what the reader needs to know NOW, in just this scene, as opposed to overloading the first scene with lots of elaborate backstory that may or may not be relevant at the moment. There's an old writers workshop cliche that most books can be improved by lopping off the first chapter or prologue and there's some truth to this. It is good that you, the author, know all about the culture and biology and personal history of your alien first officer, but don't feel obliged to try to cram it all in the first scene. Especially if the ship is on fire!
2) Consider what your Point-of-View (POV) character is going to be noticing at this moment. If the ship is under attack, chances are the captain isn't going to be rhapsodizing about the lustrous auburn hair of the beautiful yeoman, or musing about his troubled childhood on Alpha Centauri. That alien warship that's bearing down on them right now? That's
probably got his full attention. Feel free to describe it in detail.
3) In general, start with broad strokes. You can fill in the details and nuances as the book goes on.
4) As a rule, I try to at least sketch in the setting by the second paragraph or so. I hate having bodiless voices talking in a void. Let us visualize where we are.
5) As a STAR TREK writer, you have the option of being able to quickly set up the basic situation via a quick Captain's Log entry. "Stardate 3284.4. We are responding to a distress signal from a Federation colony near the Klingon border . . . ." Just keep it short and to the point. Don't go overboard trying to explain 100 years of interplanetary politics. (My log entries are seldom more than one paragraph long.)
Hope that helps.