Why didn't Allah have the Prophet Isa establish the religion of Islam while He was living on the Earth?

I have often wondered why Allah did not instruct the Prophet Isa (Jesus) to establish the religion of Islam while He was living on the Earth, which took place during the years 0 A.D - 33 A.D.. The Qur'an states that Allah performed many miracles through the Prophet Isa, so I find it a bit strange that Allah did not also instruct the Prophet Isa to start writing down divine messages, revelations, and moral laws which Allah could have dictated to him, and then Allah could have instructed the Prophet Isa to create a book from this collection of holy writings which would have become the world's first Qur'an and thus the beginning of the religion of Islam. Why didn't Allah have the Prophet Isa establish the religion of Islam while He was living on the Earth?