Iron was originally produced without melting it at all. Instead, iron ore was reacted with reduced gases, and a flux (limestone) causes the silicate contaminants to melt instead. The solid iron that's obtained (sponge iron) is then forged into shape (and also beaten to remove residual silicates.)

I googled it, and apparently we still do that, at least for some of the production.

Yes, direct reduced iron (DRI). We may be moving back to it, too, when we move to green hydrogen as the reducing agent.