I made a similar post before but as I was directed in how to make my question more focused I decided to re-write it, to be clear, Im trying to steer away from Horn/North/Western Africa, or Medieval Africa, Im asking at a period between (lets say) 1,000B.C. and 2A.D.
Now I have no problem on finding information of Medieval societies such as the Kongo, Zimbabwe, Mali and Ashanti Kingdoms, but if I try to go anywhere near B.C. most information usually ends up with the Egyptians or the Carthaginians, or the Nubians... cultures deeply tied with the Mediterranean world.
I know there have been Bantu groups in Central and South Africa for millenia, did they never develop ancient world civilizations (urban centers, trade, complex administration, writting, specialized divisions of labor) like the Mycenae, Egyptians, Olmecs, Shangs, etc...?
And if so, why? I've read about the tzetze fly as a major reason, as this pest would interrupt the development of large population centers and cattle production, but, this has never made sense to me, the Olmecs didnt had cattle either and didnt really stopped them from creating a civilization, and its not like any civilization is a stranger to disease, Central/South Africa is also bursting with mineral resources and arable land, so it makes little sense to me that I havent heard of many Ancient World Central/South African Civilizations.
Hey, I'm just getting back to this question, sorry for the delay.
Off the bat, I'm going to say that this answer is going to disappoint you. We know that there were Africans living in central and southern Africa in the period you are interested in. But, because of the limitations of data that we have, it is very hard to create a coherent narrative.
We are able to talk about medieval societies like Kongo, Mali and Asante kingdoms because we have written historical accounts from the period that these kingdoms existed. Other societies like Luba or Lunda/Ruund are written about in the end of the 19th century, but by relying on oral tradition, we are able to reconstruct these societies political and social histories back to the 16th century. Additional archaeological work in the Upemba depression can give us insights into the Luba past back to the 5th century AD.
However, for the period of time you are asking about, scholars are only really able to rely on historical linguistics and archaeology to try and gain insight about populations in that region that far back.
Unhappily, central africa is a very challenging area to work in, from a linguistic, infrastructure, and security perspective. So, it is fair to say that Central Africa is understudied archaeologically.
Additionally, in hot, humid and variable climates like the Congo rainforest or the hills of Rwanda and Uganda, or in very acidic soils, organic materials can quickly disintegrate, past settlement areas very hard to find. Archaeologists are often left with durable materials like stone tools, pottery shards, and slag from iron smelting operations.
So, long story short, a lot of the Archaeological information about the era you are talking about concerns the spread of iron and copper metallurgy from north to south. Or else it often discusses changing pottery styles and perhaps associated finds of grain kernels or domesticated or wild animal remains, to describe economic/dietary information about the people.
Jan Vansina has written a few very good books about the Congo rainforest (Paths in the Rainforest) and the savanna region of Angola and Katanga province (How Societies are Born; governance in west central africa before 1600), where he relies on linguistic information and oral traditions to try and reconstruct the development of political traditions in those regions from earliest times (optimistically perhaps 4000 years ago) to present.
Kairn Klieman has built upon his work with her book The Pygmies were our Compass: Bantu and Batwa in the history of west central africa, early times to c. 1900 c.e.. These two historians broadly present a picture in the era you ask about, of small villages of Bantu-speaking farmers organized along family lines. Klieman strongly emphasizes the interaction of these farmers with their Twa "pygmy" forest foraging neighbors, and how each community benefited from this economic/food gathering specialization.
So, to actually answer your question, as best as we can tell these societies were very autonomous and did not see the development of political units larger than the village level until the early or middle first millenium C.E.
Beyond the books I mentioned, I'd also recommend reading African Archaeology; a critical introduction edited by Ann Brower Stahl, particularly the chapters that discuss the Bantu migrations, the spread of metallurgy, and Pierre de Marets chapter "from Pottery groups to ethnic groups in Central Africa".
Edit- Also, the Oxford Handbook of African Archaeology provides chapters on late stone age and Iron age in Central africa, East Africa, great lakes region and Southern africa. However, it is a very expensive textbook, so I'd check and see if your nearest academic library has a copy of it or can borrow it. -edit.
My answer did not touch on southern Africa at all, but I would recommend Martin Hall's Farmers, kings, and Traders: the people of Southern Africa 200-1860 as an archaeological introduction to southern Africa in the period just after you are asking about.