Simple experiment. Start as Toku (Fishing + The Wheel) on small Great Plains, Normal Speed, Monarch. See starting position attached. Floodplains + Gold.
Goal: Build a Farm, a Gold Mine, and connect Gold to the city.
Research path (identical in both cases): Agriculture -> Mining -> Pottery -> Bronze Working -> Writing
Strat 1. Warrior, then switch to Worker as soon as size 2, then Granary.
Research: Agriculture (3720BC) -> Mining (3480BC) -> Pottery (3200BC) -> BW (2760BC) -> (1 turn Anarchy for Slavery) -> Writing
The city reaches size 2 in 3680BC. Worker is built in 3240BC, turn 19. Goal reached in 2560 BC, turn 36. Writing is half way through, city size 2 after Granary whipping, Warrior will be finished on the next turn.
Strat 2. Worker, then Warrior, then switch to Granary as soon as Pottery is researched.
Research: Agriculture (3720 BC) -> Mining (3480 BC) -> Pottery (3160 BC) -> BW (2800) -> (1 turn Anarchy for Slavery)
Worker is built in 3400BC, turn 15. Goal reached in 2760 BC, turn 31. City size 3, Granary is about to be whipped in a turn or two.
So, 5 turns difference. That is, 5 extra turns working a Gold mine. Even if there was no Gold, a cottage (or two, one instead of the farm) could have been built and worked 5 extra turns.
Note that Toku does not even start with Mining.