What does it mean to be a "black" civilisation. All civilisations in the classical world (this is the world stretching from Portugal to India west to east and from Britain to Kenya north to south) would have had at least small minority black populations. Immigrants, traders, mercenaries, and in the case of Egypt, occasionally (although not always) the ruling elite class. This is equally true of all other civilisations though. There were white Greeks who immigrated to places like India and Kenya.
Population movement was not invented in 1989. Immigration was not invented recently. Globalisation and globalism have been the default setting of western and southern Asia, Africa and Europe for the past 3000 years at least. Everybody moved around freely. There was no fukking border patrol or ICE to stop you from simply walking into another continent. Nationalism and closed borders and ethnostates are what is rare, unusual and weird. They're the modern inventions.
But to go back to my main point that the big cities around the classical world, especially those that were close to the sea, would have been highly cosmopolitan and their ethnic and racial make-up would look surprisingly modern to us. The only single-race ethnostates would have been in the Americas and maybe in parts of east Asia as well as the middle of Africa, because they were not connected to the classical world of western/southern Asia, coastal Africa and Europe.