Origins of north Indian classical are much more complicated than attributing to any single person. There is the Samaveda of antiquity with its puritanical emphasis on metre along with a simplistic sense of melody. Dhrupad sung in the courts of Delhi during the Mughal times can probably be regarded as the next attested continuation in that tradition. During the 17-18th century Dhrupad underwent another renaissance and the form of Khayal emerged. One which gave the musician more creative freedom of expression. A large part of what is considered mainstream North Indian classical music today is Khayal.

P.S: Amir Khusrao's role in development of Qawwali, Tarana and other forms of Islamic Sufi music making sounds plausible. Anything beyond that is venturing into speculation.