If you've ever watched a child attempt to communicate with those around him or her, you'll notice that their nonverbal cues come naturally before they are even capable of forming words. This is an ability we are born with, to use gestures with our hands, face, and eyes, to communicate our wants.
Yes, I do think that the ability to use nonverbal communications is something that is inherent. Their are certain abilities that we have that have been passed down from ancestor to ancestor that we just know. As I gotten older and had children I have notice then do things that my grandmother did and she's been dead for over twenty years.
I believe people can lack the ability to communicate non verbally. There are many adults who have problems understanding non verbal communication. I think we can clearly see that all people are not born with this ability. It is unlikely that people loose this ability while growing up. I believe it is safe to assume it is a learned trait.
A baby cries. A parent arrives with food, checks the diaper, rewraps a blanket, or any number of other things that may make a child uncomfortable. This is a basic act. Children associate crying with a response from a parent. This is the only form of communication that the child has, so it becomes the catch-all. It is not indicative of an instinctual ability to communicate, but the ability to observe and replicate for a desired response. There are cases of babies who never pick up this behavior.