The Kurdish people have existed since Sasanian times, mostly as a broad term for the seminomadic people who lived on the borders of royal authority. If these people could be motivated to move into Anatolia that might be a good option.
Have Asia Minor devastated in the endless back and forth between the Romans and Persians. Have the Kurds begin to move west in great numbers, overwhelming the Roman empire at any point when its extremely weak. That alone would probably do it, with the right PoD, especially if you can get the Romans to practically collapse shortly thereafter and the Iranian nomads can become a dominant ruling class.
Ironically, the Achaemenids are probably one of the worst time periods to try to make Asia Minor Iranian. They're just too cosmopolitan and don't care enough about cultural uniformity.
Alternatively, have instead of a the Turks an Iranian nomad group like the Hephthalites or the Rouran or whatever decide to settle Anatolia. That would work as well, and probably be less complex. If you want to see something like that happen, I wrote a whole timeline about it.
