The general consensus among audiologists is that it is not possible to diagnose a child under the age of 7. The reasons cited are usually:
The truth is the auditory system does not fully mature until the age of 12, which is really the only point that a definitive diagnosis can be given. Also, some children under the age of 7 are capable of cooperating with the tests that are required, so it doesn't make sense to draw a line in the sand based on a generalization.
School districts generally have strict adherance to the 7 and over guideline. But by that age children have definitely lost a year of kindergarten, maybe even first grade, and their self-esteem has already been severely effected by their listening challenges.
There are a subset of audiologists who believe children as young as 5 can be tested and diagnosed with CAPD. They do have tests that are normed down to 5, so they are able to administer them with appropriate comparison data. In some cases the diagnosis may be cautionary (i.e. it looks like ADP, but testing at an older age will say for sure) because the child really isn't capable of participating fully.
If a parent feels strongly about having tests done before age 7, they should seek out an audiologist who has experience in this age group. Having the testing done may not give a definitive diagnosis, but it will at least give an indication of the probability of CAPD, and the audiologist can recommend classroom accommodations based on these results.