Doing the How to HQ quest, you build a Living Quarters for 6. After that, you should have enough resources & facilities energy to build a severak 2 person Living Quarters or the Living Quarters for the Department Heads, if you build them one at a time.
You should have 10 people for the Tutorial. If you do not, you will be short resources. Use the City Manager Holotape. Go to Tools>Advanced Tools and select "How to HQ population fix" to resolve.
As your Facilities Staff grows, usually around 10 people, you can start buliding Living Quarters that can house 4 or more.
I've updated the
Floor Plans for the Main Floors (upper & lower) marking the rooms that can be 2 person, 4 person and Department Head Living Quarters.