For me it is instantaneous. I pick up a book, and from the very first sentence I'm in the book's world. Sometimes I get jinxed by thinking about 'these are just letters'. That's almost like remembering that you're consciously breathing or being aware of the size of your tongue.
But I can get rid of that within a minute of determined reading.
On a related note, if I'm sick and I manage to get into a book despite the initial discomfort I can ignore my pain/sickness completely.