pretty much impossible.
take iron bloomery, consolidate it from a smelt into an ingot through several forging passes.
then convert, of "fine" it into blister steel. That's formed by roasting the wrought bar iron in contact with carbon (usually bone dust and similar) in a cementing furnace. Its so called from the resulting blistered appearance.
To improve the quality further, it is subjected to two subsequent processes, which convert it into shear steel. that's done by taking multiple bars of blister steel, binding them together, and then forge-welding, folding, and rewelding.
higher quality for blades can be made by repeating that process, making what's called Double Shear steel.
Lastly, ingots of blister steel can be placed into a crucible with broken glass, and a small piece of charcoal, sealed up and then heated to white-hot. the steel melts, and impurities are fluxed into the glass, and carbon is transferred from the charcoal (which also burns, briefly, consuming the oxygen in the crucible.). the result is "cast" or crucible steel (note "cast steel" in this case is not in fact, cast in the sense of casting in a mould. that process is much later and different.), which is then forged out into blades.
more advanced crucible steels are made with particular alloys, resulting in cementite banding inside the steel, which becomes "Damascus", or "wootz" or "pulad" or "bulat".
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but the idea that steel would be lost while they can make iron is utterly absurd. Even a simple tatara furnace for smelting can produce high-carbon steel native straight from the raw ore. Lower carbon wrought iron is more common, but any good smelter can at least get some steel along with the iron.