I am not sure I can explain why, but only only "self-sufficient enough" works here. But even better is just "sufficient" or "enough". The idea is that there is some minimum level of self-sufficiency required and the words "enough" or "sufficiently" express the attainment of that minimum level. By the way, the first phrase really doesn't say much. When we talk of "civilization" it is obviously civilization on Earth, which is obviously a planet. So you could just say "There was a period in history known as the "primitive communal system [epoch or era?]" wherein a tribe of several dozen was sufficient to form a state. " Of course if there is science fiction and you are comparing this to other planets, then you need the reference to Earth. Does that help?

Here are a couple of examples using ENOUGH this way that may be easier to understand: He doesn't earn much money. He is not rich enough to buy a house. She is not old enough to drive a car. I'm not smart enough to be a rocket scientist.

In the historical development of human civilization on planet Earth, there was a period known as the “primitive communal system.” This is when a tribe of several dozen people were self-sufficient enough to form a state. I ended your sentence after "primal communal system" because adding another comma makes it a run on sentence. I added a "This is" because I made it the start of a new sentence. Lastly, I changed 'was' to 'were' because you are talking about the past. Self-sufficient enough is fine. If you wrote "This is when a tribe of several dozen people were self-sufficient to form a state" it doesn't make as much sense. The word 'enough' clarifies to the extent that they were self-sufficient.

'Self-sufficient enough' is required to make sense here, but you could use Tom's suggestion of 'sufficiently' by saying 'sufficiently self-reliant'.

In the development of human civilization there was a period known as the “primitive communal system” in which a tribe of several dozen people was sufficient to form a state.