I’m thinking I would go with either, “swing it, baby” or “right on, sister!”
So, like-
“Mr. Nartik, set course for Tau Alpha III. Warp six.”
“Course laid in, sir.”
“Right on, sister!”
This would be the 23rd or 24th century gender-neutral form of the word sister, obviously.
ricecake, Whelp, it’s about that time.
[Gently slap thighs]The ship will actually depart in about 45 minutes.
Dasus, This would be the 23rd or 24th century gender-neutral form of the word sister, obviously.
We already have one: “sibling.”
That being said I’d probably just go with “engage” and “hit it” varyingly. And when using “engage” I’d hope to emulate Picard but in a way that wouldn’t make people think I am.
FlyingSquid, 
It was a joke, my friend.
Dasus, Yes, I understood it was a joke.
That doesn’t prevent me from commenting on it, though, as the premise wasn’t bad, but the example given wasn’t the best.
limelight79, Let 'er rip!
FlyingSquid, Theme song by the Dead Kennedys!
Etterra, If I had a ship with variable wrap geometry: transform and roll out!
kuneho, 
“Akkor zsa”
showmeyourkizinti, Honestly? “Make it purr, not number one”
EmpathicVagrant, ‘Sgo!
chuckleslord, “Yep”
“Mmhmm”
“Theramin”
“Let’s go, slappy”
gregorum, “Let’s do this”
Strayce, (edited ) I’m Australian so I’m legally obligated to go with “Fukken fang it carrnts!”
wahming, Fart sounds. On the shipwide PA system.
Evil_Shrubbery, What’s the sound for red alert?
wahming, For each alert level, increasing amounts of wetness
spittingimage, 
“Begin”. I feel like terseness is a virtue on the command deck.
Kolanaki, 
silently presses the button that makes ship go
Oddbin, 3,2,1 ACTIVATE!
gregorum,
edgemaster72, 
This just made me realize the first 15 seconds of the Cowboy Bebop theme would be a killer way to do this. “3, 2, 1, Let’s Jam”
LopensLeftArm, 
“Wubba-lubba-dub-dub!”
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