I think you're underestimating how spectacularly hard it is to make anything without tools. Go into the woods naked, and show me how to make a bellows.
I'm pretty sure i could do it, if i could keep my glasses, and my shoes and a knife and a bunch of food. I think i could run down a deer, if all the other people i'd be in competition with didn't kill me after i was 10 miles into the run.
I don't think steel matters very much. Sanitation, clean water, lots of food.
"If society knows about existence of a technology, reproducing it shouldn't be difficult. The hardest part about progress is inventing brand new things."
I disagree. Once upon a time, people drove cars on the moon. Should be a n easy thing to reproduce eh? heck, we've got 40 years of technology on them. The hardest part about progress is convincing other people to do what you want them to do.
The gingery books are FANTASTIC. i'd highly recommend them to ... everyone.