If Babylon works how we think and they instantly finish any tech they get a eureka for we need a list of hilarious beelines for absurdly powerful unlocks.
settle coast for Sailing unlock, 2 coastal resource to unlock Celestial Nav, 2 early Harbors for Cartography
3 fast archers to get Machinery for ancient era Crossbowmen
kill 3 barbs to reveal Iron, then build a mine for Ironworking
start game researching Animal Husbandry, get a builder first, then a pasture for Horseback Riding and Horsemen available by turn 10 or so
mining, builder to start game, build 3 mines and laugh at Gaul as you unlock Apprenticeship by turn 14 or so
3 early workshops for instant Industrialization which reveals Coal
build classical coal mine to unlock Steel
two coal plants for Refining which reveals Oil
build Oil well to get Plastics and upgrade your scouts to 60/65 str SpecOps (maybe in medieval?)