It depends on the map and my starting position.
I have a hand-picked, carefully pruned starting seed world I’ve been choosing, and I always start in areas that are inaccessible or semi-inaccessible, I pretty much know exactly where I’m going to dig, etc.
Because of that I’m able to beeline to blacksmith pretty quickly, and I can also put off getting a footman for a long time.
So, looking at my most recent set of saves, in that scenario, looking over old saves, it looks like I had a blacksmith at the beginning of Day 3 – essentially as soon as I started digging – but didn’t bother with a footman until Day 7. By Day 10 my blacksmith was working on steel gear, so there were only a few short days where he was in bronze or iron (I never bothered with iron armor at all).
Day 3 blacksmith setup is carpenter, farmer, mason, trapper, 3 workers.
Day 7 footman is blacksmith, carpenter, farmer, mason, trapper, 3 workers, soldier.
I think that whole calculation probably changes if enemies have ranged attacks and I can’t just be 100% safe by climbing halfway up a cliff face and huddling my dudes in a blob at the top of the ladder.
That said, the big hurdle with the blacksmith generally isn’t just having the blacksmith; it’s moving beyond bronze gear into iron and steel. This is entirely dependent on whether there are convenient veins in the locations you want to dig and/or there’s an early Rufus Garrow you can buy a load of copper/tin from to make that first blacksmith’s hammer and get rolling.
The other consideration is that once you do have a footman armored up in top-end gear they trivialize absolutely everything. That’s probably just as well given the rudimentary nature of the combat right now but as far as I can tell a single footman with platemail/shield/helm/two-hander can obliterate an infinite number of everything in this game, up to and including necromancers, goblin armies, etc.
Net result is that right now the combat isn’t really that challenging at all either way. The first few days, your hearthlings can handle everything that might happen just by blobbing up; after that, your footman is very quickly in the top end gear and everything is trivial.