What do you think is the ideal number of players? I really want to get a game going, but I feel like because of the way roles work in ST you really sort of need at least ... 4? And probably better for 5 or even 6? Most rulesets you can modify for fewer players but I don't think it's possible with STA sadly.
I’ve run the game for four, five, and six players, and played in groups of three and four. My current group is five players, and I am strongly considering trying to find a sixth, as the NPC chief engineer recently ”Stayed at ‘er post!” and I do think it’s a role that would benefit from having the players take it on, whether that means a new player or the players making a new support character.
But to get to the heart of your question, I think you could run the game for a group of three without too much difficulty. Consider TOS where most of the episodes focused on Kirk, Spock, and Bones. If your inclination as a GM is that the players are doing a lot of away team missions, I think two or three characters are completely viable. And for groups that small, the core rulebook recommends that when it comes to space encounters that each player control a support character as well as their PC.
Support characters are the STA special sauce, so far as I’m concerned. I know Modiphius’ other 2d20 games have the same mechanic, but in STA it really functions so that the players aren’t just running their main characters, but the entire ship. It would be like if TNG was a tabletop game and Worf’s player realized that there wasn’t going to be a lot of combat going on this week as they deal with an engineering problem, so they grabbed the O’Brien support character from the shared pool.
And I think with a lower number of players, the support characters are going to work to fill out the crew as needed.