Options: they worked on a large cargo freighter, saved up enough money to buy a ship, set out on their own. They crewed a smaller ship and the captain died, retired, or is out of the picture in some way. All are freelancers hired to do a job. Time share spaceship. Reality TV show.
I like the "vanished captain" option. It explains why we suddenly found ourselves with a ship on our hands and simultaneously provides an intriguing plot hook. Was our captain involved in some shady deal gone wrong, did he stumble upon something worth killing for, or is he just lying drunk somewhere? Characters who don't fit as ordinary crewmembers (Dr Puddington, etc.) could earn their place onboard by helping us get away with the ship, before we're caught by the authorities (strictly speaking, it might not be
our ship to just sail off with) or whatever it was that disappeared the Cap.
EDIT: A focused "Hell Out of Dodge" prologue would let us familiarize ourselves with our characters, the setting and the game. Then, once we've escaped into space, we can have an in-character discussion about what to do next and how to go about it.
If people can take it in stride, then I think it might be cool to let
all the proposed characters participate in the Prologue. Then, at the end of the Prologue, the GM would select the most active/creative/sensible/funny PCs that would make it onto the ship and into the rest of the game, and set up some reasons why the others didn't manage to get onboard. It seems like a reasonable way to evaluate the PCs and players, while for those who are not chosen, being in the Prologue is still better than nothing, in my opinion.
EDIT 2: On second thought, I can also see several reasons why a knockout prologue might be a
bad idea (drama, unwieldiness, hard to merge with in-universe events). An ordinary waitlist is probably a safer bet. I still like the other ideas, though.