Muslims are not descendants of Ottaman Empire.

Ottaman Empire was a major Turkic muslim empire during the Gunpowder empire age. Along with Turkish people it had many other ethnicities under its rule - Kurds were one of them.

The other gunpowder empires of this era - the Mughal empire (based in South Asia) and Safavid empire (roughly around modern Iran) - were also Muslim empires.

Islam as a religion started way earlier - in 7th century - in region of Hijaz which is part of modern day Saudia Arabia.

Kudrs are an ethnicity that while mostly Muslim, also have minorities following other religions. Ayyubid dynasty was a major Kurdish Muslim empire that has highly influential in fighting back the crusaders. As a distinct ethnicity they are much older than Islam.

If you're thinking why is Ottaman empire's image so closely related to Islam - perhaps because it was the last major Muslim empire to fall to Europeans. After that even when "Muslim countries" gained independence it was as nation states based on European models. Many parts of middle east however ended up with Monarchs placed in power by British instead.

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Muslims and Islam is much more than just some empires. Countries like Indonesia and Malaysia were never conquered by any foreign Muslim forces. And many Muslim countries even to date have minority religions communities - there are many Christian Arabs. Even by start of the crusades, Egyptians were mostly Christian. The Mughal empire mentioned above was actually majority Hindu. :)