As far as I understand it, you should receive a bridge officer, but I can't say for sure since I had the same problem. It's not a huge train smash given the availability of them, but it's somewhat annoying.
Under normal circumstances, I believe you'll receive a mission in your quest log to accept the incoming Boff.
Did you check in your character menu (U) in Stations and look to the right to see if any are listed there? My wife had the same problem
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I believe it's just that the slot opens at level 5. You still have to hit a mission which rewards a Boff to actually add one; otherwise, to fill that slot, you need a C-store boff or a regular one an alt can send you.
Keep calm, and continue firing photon torpedoes.