Alright so we're looking at 10 Civs per era, huh? So time to make some real guesses:
Han | Ming | Qing |
Khmer | Majapahit | Meiji Japan |
Maurya India | Chola India | Mughal India |
Achaemenid Persia | Mongolia | Safavid Iran |
Mississippians | Hawaii | America |
Greece | Normans | Britain |
Rome | Spain | France |
Egypt | Abbasids | Buganda |
Aksum | Songhai | Russia |
Maya | Inca | Gran Colombia |
Greece -> Norman/Spain/Inca(if mountains), Normans -> France/Britain, Spain -> France/Gran Colombia
Rome -> Norman/Abbasids, Abbasids -> Buganda/Safavid Iran
Egypt -> Abbasids/Songhai/Mongolia(if horses), Songhai -> Buganda/France (for the city-of-lights on the river, not the colonization), Mongolia -> Russia/Mughal India
Aksum -> Chola India/Abbasids/Inca(if mountains), Chola India -> Mughal India/Safavid Iran/Britain (for the seafaring, not the colonization)
Maya -> Inca/Shawnee/Spain(if no Shawnee), Inca -> America/Gran Colombia
Mississippians -> Hawaii/Inca/Shawnee/Songhai (if no Shawnee, for the rivers), Hawaii -> America/Meiji Japan
Han -> Ming/Hawaii(if coastal)/Mongolia(if horses), Ming -> Qing/Meiji Japan/Russia
Khmer -> Majapahit/Chola India/Ming, Majapahit -> Meiji Japan/Mughal India
Achaemenid Persia -> Abbasids/Mongolia/Ming(if huge population)
Maurya India -> Chola India/Majapahit(if coastal)/Inca(if mountains)
Shawnee -> America/France (rivers again)/Gran Colombia (confederation of states)
I'm going to keep refining this but I'm happy for now.