You can start producing stone from the Bronze Age from the "Stone works" unlockable there, you don't actually need to have the resource to produce goods in a goods building, it increases the amount you can produce but it is not necessary to own the resource to produce the goods.
The improved stone works building is slightly smaller in size but also produces goods at twice the rate of the Bronze Age stone works so instead of getting 1 stone for 4 hours work you in fact get 2 stone per 4 hours. So by the time you come to unlock the improved stone works you should have plenty of stone made from the earlier building.
Hope that helps explain it.