Should fabricating a forge be possible without finding specific tools?

For any kind of vehicle work, or advanced fabrication you need a hacksaw and maybe a hammer as well (to craft a forge). You can craft everything needed to craft a hacksaw with a (acetylene) torch and a hammer. You could then use those to craft your forge. Would it be a bad idea to make them craftable from scratch instead? You would need to change the tools required to need hammering of 2 and allow makeshift wielders to craft them. The crafting line is still restrictive (a twelve item crafting line) and requires alot of tools, or skills to craft those tools

Theres two ways of making the forge craftable from scratch, you can either add makeshift variants of hacksaws, and wrenches. Or you could change the tool’s existing recipes to be craftable with a makeshift welder. You might also want to make screwdrivers craftable with a welder too, so that you don’t require ducktape. You could call the ducktape variant makeshift and take away its fine screwdriving quality. It doesn’t make sense that a bunch of scrap held together by ducktape would have fine screwdriving anyways…

Makeshift welder/ (antenna/ screwdriver >) soldering iron > crucible > anvil > tongs > chisel
(1) makeshift tools > forge > s&d set > hammer > hacksaw
(2) s&d set > hammer > hacksaw > wrench > forge

This is good for characters that want to avoid diving deep into towns, people that want low item spawn rates or simply got very unlucky with their item luck. I just find it hard to believe that a blacksmith, with 4 or more fabrication, can’t make a forge from scratch with enough steel. I’m not sure how useful it is since it seems a bit flimsy, but surely you could make it more sturdy with thick wood, sharpened steel and nails/ ducktape. Thoughts?

Edit I: Forgot to add a wrench in the second example.
Edit II: Edited to make what I was suggesting clearer.