Simply put: it is very unlikely that a distinct ethnic group known as "kurds", or any direct antecedent, existed that far back. The word "kurd" simply means "tent-dweller" or "nomad" and was applied in Islamic times to seminomadic speakers of Iranian languages (with Kurdish descending from these languages). It is to my knowledge unclear when exactly the Kurds emerged as a distinct ethnic group traceable to this day, but at minimum, it was some time after the Seljuk invasion and the influx of Turkmen south of the Caucasus.

What you'll be looking for instead is any number of ethnic groups, principially West Iranian ones with a similar lifestyle in what is today Kurdistan. One often sees mentions of "Northwestern Iranian languages" but this is not really a proper linguistic group with a common ancestor, it is just a term of convenience for West Iranian languages (which is a proper group) spoken in the vicinity of Kurdistan.

I am not sure exactly what you need this information for (schoolwork? curiosity?) but I would start my research here, with Encyclopedia Iranica's "Kurdish Language" article. Let me know if you need elaboration on anything.