There are some interesting combos for classical or medieval rushes, even without strong unique units. Obviously map-dependent:
Willem of India - with instant 3 commerce tiles and starting with mining could go straight for BW and chop out axes extremely fast. Think settling on a riverside wine or dye or something with maybe an oasis to work. Creative just makes it easier to get bronze in a useful spot, it could be any financial leader I guess.
Pericles of Korea - with mining/myst instead of Greece's horrible starting techs and how quickly you can get your first scientist out and bulb Maths...it should be possible in many games (up to immortal, maybe consistently on Deity on handpicked starts) to oracle Construction and go crazy with Hwachas.
Boudica of Rome - as if Praetorians weren't already way overpowered, CI/CRII after a single successful attack. CI/CRIII Praetorians are basically unstoppable until macemen and you'd get there quickly with the high attack odds you're already getting.
Hannibal of Rome - as above but you lose the free combat promo and insta-barracks in exchange for faster IW if you have early commerce tiles.
Suleiman of China - Engineering rush with Cho-ku-nus.
Churchill of Spain - cheap Citadels for CRIII charismatic trebuchets from every city.
Sitting Bull of Spain - cheap Citadels, can bulb Machinery but not Engineering.
Suleiman of Spain - no cheap Citadels, but can bulb Engineering. Would be pretty good if you had stone.
Churchill of Mali - protective skirmishers that get to Drill III/IV quickly, could be a viable rush even at high difficulties.
Sitting Bull of Mali - Drill III skirmishers immediately.
Could do the same with Babylonian bowmen, might even work better at Deity where you might face more metal units than archers but the target would have to be very, very close.
Ragnar of Sumeria - aggressive Vultures that you could get to very fast, again with the right tiles in your capital.
Darius of Sumeria - fast vultures, even cheaper Ziggurats.
FDR of the Aztecs - Oracle CoL with no need for marble, get cheap Sacrificial Altars.
FDR of Carthage - on any sort of archipelago or islands map. Fast GLH/Colossus, cheap lighthouses, Cothons....
Churchill of the Celts - I'm trying to convince myself that fast Guerilla III units would be interesting. It's a stretch, those starting techs are so so bad. I guess it would be fun to have upgraded Redcoats with 50% withdrawal chance?