Normally they won't do a formal assessment under the age of 7. That isn't unusual. Clearly something is going on though.

My own son was assessed at late 6 early 7. The assessment was started due to severe speech delays and severe fine motor deficits. In the course of testing, the psychologist also saw the ADHD. His formal educational diagnosis is OHI(Other Health Impaired) for ADHD. That allows him to receive special ed services, including occupational and physical therapy, counseling, speech services, accommodations, etc.

He his all of these issues that play off of each other and complicate each other which kind of sounds like what may be going on with your son. Some of what your son is showing might be ADHD, but there certainly seem to be other issue complicating things, and unfortunately it can take time to get accurate assessment on young children as there is a wide range of what is consider within developmental "normal" at that age. That range gets narrower as kids get older which is why it is easier to assess kids as they get beyond those early developmental years.