No, not really, but thanks.
Unfortunately, no relevant information is found.
can you give me an idea of what documents should I show as proof that my child doesn't have a social security number?
Sure. If your child lived in another country then you can use his current or previous passport as proof, or you could use his school records or how employment records in that country. Any document that shows your child lived in another country for an extended period of time would work.