In an interview with JK Rowling she answered this question.
... Also how does the Ministry of Magic find out these kids have powers? ... JKR. The Ministry of Magic doesn't find out which children are magic. In Hogwarts there's a magical quill which detects the birth of a magical child, and writes his or her name down in a large parchment book. Every year Professor McGonagall checks the book, and sends owls to the people who are turning 11. (source: Online chat transcript, Scholastic.com, 3 February 2000)
And yet Nevil was unsure if he was a squib or not until his letter arrived.
If the parchment is a list of all magical births, why are squibs either not known, (due to their exclusion from the list) or the information is restricted? It seems the family would want to start making plans for their child as early as possible.