A further thought on Muhammad copying the Infancy Gospels

Muslims are quite right, of course. There is no proof that the author of the Qur'an was inspired by the stories found in the Infancy Gospels.
If there were, then presumably all intellectually curious and well educated Muslims would have abandoned their faith. (Instead of just some of them...)
I am suggesting, however, that the balance of probabilities tips ever further towards the very strong likelihood that Muhammad (and /or others) was the author.
I find it pretty much inconceivable that stories relating to the childhood of Jesus, unknown until the 2nd or 3rd centuries, written at just the time when Christian teachers were in need of fantastical tales to keep the faithful happy and found in a collection of otherwise preposterous pagan fantasies, regarded by scholars as having no connection to the historical Jesus and circulating in Arabic in the area and at the time of Mohammad... should happen be true.
Call me an old cynic if you like and let your God burn me in Hell for an eternity for being so... but where is the argument to convince me otherwise?