Not sure why your comment was dead since it's a good question. The answer is with charcoal, which is how it used to be done. It's less efficient (charcoal isn't as strong as coal so the furnaces have to be smaller) but it worked fine in the past. You obviously couldn't have the same steel output using charcoal. In the past places started running out of trees to turn into charcoal which is why they switched to coal in the first place.

In Sweden they are building a prototype of the Hybrit process, using hydrogen to reduce the ore. The plan is to convert the blast furnaces in Sweden and Finland within a couple of decades.

Now this isn't a particularly low tech way of going about it, and producing the hydrogen requires massive amounts of electricity. So probably not an option if you're bootstrapping civilization after a collapse.

The article goes into detail about how Brazil is creating steel without coal right now.