You could argue that the tribal confederacies of the Black Sheep and White Sheep (Kara Konlyu and Ak Konlyu) were Kurdish states. They certainly had a signifcant amount of Kurds in them, and a Kurdish elite. At this time, however, the term "Kurd" was more of a social term (designating nomadic Iranians) than an ethnic term.

The Ak Konluy conquered most of what is today Iran before losing out to the Safavids (who themselves has some Kurdish roots) and eventually being conquered by the Ottomans.

In the modern sense of the word, the Kurds have never had their own nation state, but they have been part of the elite of a Confederacy that included their land, and before the islamic conquest, they has several independent tribal principalities in the region.

nation states as we understand them didn't really exist before the French Revolution. People tended to think of themselves as either citizens of their city, subjects of their king/emperor, or members of their tribe. That being said Kurds were by no means bared from leadership positions in many middle eastern realms. Saladin the conqueror of Jerusalem and founder of the Ayyubid Sultanate in the 12th century was Kurdish for example.