How to unlock the blacksmith in Nioh 3
You unlock the blacksmith after completing the first crucible dungeon and defeating Jakotsu-baba, the boss at the end of the "Hamamatsu Incident" quest. This opens the Eternal Rift, Nioh 3's central hub, where the Fox-masked Blacksmith is found in the building to the south.
Speak with her to forge weapons, armor and tools, remodel equipment, and disassemble items for resources. Disassembling gear yields crafting materials that are often more valuable than the coins you get from a Sudama merchant, so it is usually better than selling unwanted equipment.
Soul Match and Soul Extraction start greyed out. To enable them you must begin the blacksmith's myth, "A Fierce Flame," by talking to her and following the objectives: visit Lake Sanaru in the Warring States period, find a Scampuss that will take you to loot Kagutsuchi's Magatama, and bring that item back to the blacksmith.