Well, you don't ever have to have an anvil. Nor a pick.
IF you are going to be a surface dweller, no pick needed. You can use wood and plants from the area, and wherever you start, you get 3 wood out of the starting wagon, so that's a carpenter's workshop (1 log), and 2 logs left for whatever (training axe to cut trees to start your lumber industry, for instance).
If you aren't going to bother with metalshops, you don't need an anvil.
It is possible to build a highly successful surface or suspended fort using only wood and surface available resources. However, you do have to look out for a few things. Such as: No stone means no early mechanisms nor anything that depends on that. No stone and no metal means never any mechanisms. No mechanisms really hurt my fortress defense abilities, so I find it very challenging (no traps, no drawbridges (NO LEVERS OR LINKS!), no traction benchs, etc).
With clay, you can make a LOT of stuff, and clay is often available to surface. With sand you get glass making.