Once a student officially enrolls in a course in Axess, the student will typically be added to the Canvas site within an hour. Canvas processes 500 events every 30 minutes (top of the hour & at half hour mark), so the number of updates in the queue will affect how quickly the student is granted access to Canvas. It may take longer when there's a large number of updates needing to be processed.
If a student doesn't see the course on their dashboard, they should check Courses > All Courses to see if the course is unpublished or see if they've favorited courses that does not include the course they're looking for. To include or remove courses from one's Dashboard, steps can be found in the help guide, How do I customize my course list?.