In order to learn non-verbal communication, the brain has to take a bunch of incoming sensories and package them all together into a social-emotional meaning, such that future occurrences of those sensories are matched to the learned pattern of sensories to quickly get the social-emotional meaning, and the details of the incoming sensories are no longer individually perceived, but rather as the holistic social-emotional meaning. Then, details of incoming sensories that don't fit the learned pattern of sensories are filtered out and not perceived at all, such as non-native speech sounds being filtered out, while native speech sounds are locked in. So NT children become more and more synchronized with each other as these patterns are established, until NTs all share a set of non-verbal cues meaning a set of states of mind by adulthood.
The brains of autistic children are probably not packaging the sensories into the social-emotional meanings inherently critical to the NT brain, so the sensories remain sensories, and the physical details continue to be perceived individually, without being converted into a holistic social-emotional meaning that pops up quickly in your mind for you to sustain a flowing real-time interaction using non-verbal communication. Perhaps this lack of filtering out and locking in eggsplains why autistic adults have been measured to have greater discrimination of sensory details, such as for pitches and contours of sounds in music. Too much discrimination of eberry single sound eberrywhere is probably not good for perceptions of connected speech with its very limited set of sounds, as eberryone with auditory processing problems knows. By a certain age, autistic children who have not learned non-verbal communication the NT way can still learn the non-verbal communication and states of mind of NTs by observation like watching TV and reading fiction which is like watching TV for many, and formulate a facsimile of NT ToM that they can apply for socialization, but missing many of the subtleties of NT states of mind, I think based on my own eggsperience. Certainly I can socialize with others and even successfully as long as I am behaving naturally like myself, but I am operating using a simpler ToM based on the one that NTs and autistics share, the one that involves basic strong hoooman emotions like happiness/sadness/anger/fear, rather than the ones that NTs share with each other and not with me, involving more complex social-emotional meanings like social hierarchies or power play or external validation and invalidation of each other or subtle emotional eggschanges.
I know one possibly autistic person, and we don't use non-verbal communication with each other. We talk while walking down the street without looking at each other, and we also sit on the same side of all tables. There is no need for non-verbal communication when whatever comes to mind can be freely spoken in the absence of the NT social-emotional context that disallows some thoughts from being spoken and therefore admitted.
Btw, I just made these idears up based on own eggsperience and the literature I read.