Babies are unconscious then are some point they are. That's the mystery, and why my use of the word initial is appropriate. How do I trigger the process of consciousness, does it occur automatically once all the pieces are present, perhaps, or does it need a bootstrap or pilot light. Interfering with part of a brain to cause unconsciousness is super interesting, but by itself it doesn't give us all the answers. (nothing ever does)
If you want to talk about mechanisms, like recursion, then we're going into theory. Theories which I don't have the resources or capabilities to test on my own, so I don't really wish to speculate too deeply there. Maybe it emerges gradually, maybe it is quick like waking up. No idea, but it seems that part of what happens is testable. Should be an interesting future when we find out more.