I am not an expert on single player by any means, but I think the snowball effect of getting that hammer from the start is more important than having the extra hammers from the mine later on.
For example:
Assumming you go work boat first...
By settling on the plains hill you can work the plains forest for a tottal of 1 food & 4 hammers per turn. Thus getting the workboat in 12 turns and gaining 12 food towards size 2 in these 12 turns.
If you compare that to settling on south fur for example and working the plains hill to get the workboat...you are -12 food in the first 12 turns already.
This means that after improving clam you will grow size 2, 3 turns later....which means that you will get worker 3 turns later, which means that you will get fur improved 3 turns later and so on.
Also in this situation you will have 6 hapiness after wheel. At size 6 lets say you will be working the 2 furs the 2 clam and 2 hills...the third hill will come in play much later after monarchy, way after monarchy since you will be working cottages etc..
So unless you plan to neglect furs and work 2 clams and 3 hills from early to make wonders...then the mine will take a veeeeery long time to catch up to the extra hammer..if it ever does.