I suppose it would be if you farmed a large enough area.
Just gather enough seeds with the herbalism skill to make a huge above-ground farming plot. If you gather enough, and make the plot big enough, you might be able to get enough produce together to buy an anvil.
It. Is. Not. So. Easy.
You do
not get the seeds by Herbalism. You get plant food, and then you must wait for your dwarves to eat those plants to get the seeds. And Farming does not provide you with seeds either and nor does Cooking and you cannot Brew because you haven't got a barrel. So you effectively get an average of 7 seeds per 2 months no matter how many plants you have. Forget about large-scale farming, you won't make it.
The only exception is starting in a swamp and going for rope reeds. You can Process them in Farmer's Workshop and you get the seeds by doing that and with the thread you can start a small clothing industry (rope reed farm, farmer's workshop, loom, clothier). This is exactly the route I tried on my second attempt - but I still failed to buy the anvil.
Cooking extra plants may indeed provide an additional source of income though. It was a mistake to keep them for my dwarves to eat - I hoped to start a parallel food farming project.
Anvils aren't all that expensive, just produce an inane amount of crafts and you'll be set. Also, alcohol roasts are a great trade item.
And the raw materials for the insane amount of crafts come from where? Also forget the alcohol roasts because you won't have any alcohol.
Well your starting seven could be drafted, then have your trainee wrestlers maul some poor animal to death, use the bones to make a crossbow and some bolts.
That is an option but wild animals are a very limited and unpredictable source. At least I didn't get any wild animals on both attempts (actually on the first attempt I did get a horde of carps in the river, but I didn't dare to go wrestle them unarmed and unarmored).
(Your using the wood from the wagon to build the depot?)
Not immediately. Caravan comes in Autumn, so until that time you can build virtually anything. You just have to keep track of time and deconstruct everything in August to build the Depot before the caravan arrives.
This is totally possible on most biomes, just not in ones that are completely devoid of water and flora, or full of bloodthirsty skeletal elephants and the like.
Seems you totally misunderstood the challenge. The problem is not to survive until the first caravan comes - this is the easiest thing. The problem is to earn enough to buy an anvil and a pick from the very first caravan - which is not as easy as it looks.