I see you are talking about grade school (grades 1 to 6). I agree "auditing" is rarely done there. But that is because "auditing" has no meaning in American grade schools. There are no "credits" to receive. You do not need to complete "credits" to move to a higher grade next year (like high school and college). At the start of each year, each student is placed in the class they are "ready for". Some repeat a grade. Some skip a grade. A student new to the school may be placed in any grade.
The only exception I can think of is the one you propose: a student is too young to officially attend the school. But an exception is made, allowing them to attend grade 1 classes. The words "audit" and "auditor" seem appropriate, but probably would not be used. Instead we would say they were "allowed to sit in on the classes".