Rogue Trader is one of those settings where this kind of question is quite fundamental to how you run your campaign. I am actually GMing a long-term Rogue Trader campaign myself and although I have 7 regular players, I still have several key roles that remain unfilled by players (Void Master being the notable one).
In my case, I decided to quite extensively write up NPC crew members for not only the missing Rogue Trader archetypes, but also 2-3 prominent underlings for each PC, each with one or two bullet points on personality and agenda. In my particular campaign, the PCs had only just come to power on their ship and it was somewhat controversial, which gave me a lot of opportunity to bring them together as a group against a common adversary (their mutual rivals aboard the ship).
The thing is though that you want the game to be a story about the players, which takes place in an engaging, believable world. You don't want the game to be about an engaging, believable world that happens to contain the players; notice the subtle difference there.
I think in your case, this being your first attempt at being a GM, you have probably chosen a hard setting, but everyone has to start somewhere and this is by no means an impossible task, especially if you and your players are already familiar with the setting. Your players have actually chosen 3 roles that work very well together, as all have common interests and activities (Who keeps the arch militant's soldiers fed and armed? Who keeps the Rogue Trader safe from dark hold mutants, ambitious rivals, and warp-crazed crew mates? Who signs off on the Senechal's acquisitions and gives the okay for their covert operations?).
My advice is to make a "cheat sheet" of some prominent NPCs with whom the PCs will interact on a regular basis. At least 1 for each of the archetypical roles, and a couple of underlings for each of them. Make sure you have at least one rival / villain in each of those lists, to give your players something to struggle against and overcome. Try to make sure it's somebody they need so they can't just vent them out the airlock into the void at the first opportunity (or not, if that's how you'd prefer to play it).
I recommend for each NPC you note their archetype, role and title aboard the ship, and 3 bullet points about personality, history or agenda. Leave a couple of lines for each one to fill in additional things that come up in game.
In my campaign, one of my PC's current favourite NPCs is the spoiled teenage son of the Rogue Trader's cousin (one of her main rivals), who they torment by giving "positions of honour" that are actually quite inconvenient (Lord Commissioner of the Waste Management System, Chief Curator of the Trophy Room of Oddities, Fire Safety Awareness Advocate, etc.), and set up for failure.
The most important point of all is to relax and enjoy the ride :)
Best of luck!