Considering how rare hammers are in this game, mines are supreme. I think the game counts on multipliers to make the mines more appealing as time passes, which is something food deoesn't get. For example: windmills, factories, etc. Besides, you can only build them on hills anyway.
And no, I didn't say build workers after you researched the tech.
Build a worker sometime before they get the tech. Ideally, you could steal a worker from someone before then with your warriors. In fact, I definitely recommend immediately declaring war on nearby players. I mean, they don't do anything for you and you can bet your arse you'll be fighting each other. Since we're counting on our military strength and skill to be superior to theirs, might as well get started early right? You could park a warrior just out of range of their city on a forested mountain and they won't even dare to upgrade their city tiles. Eventually if you feel you can't beat them (if you can get an early spearman from a ruins, you can easily kill them off with a single medic upgrade), just accept their ridiculous terms of surrender.
Not to mention that declaring war super early on a nearby fellow means that other person hasn't met other leaders yet and can't make them hate you for declaring war.
Not to mention the ai sucks at combat, so it'll be an easy win.