Please exercise some common sense. Populations grow significantly over generations; 800 years is a long time for a population to dramatically expand. Also, if you actually go back and bother reading actual historical sources rather than just making baseless conjecture, you’ll realize that there was actually a fairly significant stream of Muslim immigrants to the Subcontinent for centuries. Remember, during its heyday, Mughal India was the world’s wealthiest state - salaries and jagirs were very lucrative, and Middle Eastern/Central Asian noblemen, scholars, and artists were given clear preference in Muslim courts throughout South Asia. At the height of Mughal dynasty, immigration to India from Iran was so rapid that some Iranians (somewhat hyperbolically) feared that the entire Iranian aristocracy would end up leaving for India.
It’s rather evident that you don’t know what you’re talking about. First of all, Kashmir is actually a very poor example. Compared to the rest of South Asia, Kashmir has a relatively lengthy history of self-rule. For most of its history of Muslim rule, Kashmir was ruled by native Kashmiris/Ladakhis who had converted to Islam under the influence of Central Asian & Iranian Sufis. And second, Muslims claiming foreign descent (referred to as “khandaani” families in local parlance) are a significant portion of the Kashmiri Muslim population