It seems as though the process actually works the other way 'round: children are assumed to be Squibs first1; so the question really is, when is a magical child definitively proven to be magical. The answer is kind of annoyingly unsatisfying:
As soon as they show strong accidental magic
The deciding factor, at least in Britain, seems to be Hogwarts' Book of Admittance and, in borderline cases, it errs on the side of "assume Squib until dramatically proven otherwise." The Pottermore article on the subject, for instance, remarks of Neville Longbottom:
A mere whiff of magic suffices for the Quill. The Book, however, will often snap shut, refusing to be written upon until it receives sufficiently dramatic evidence of magical ability.
Thus, the very moment that Neville Longbottom was born, the Quill attempted to write his name and was refused by the Book, which snapped shut. Even the midwife who attended Alice Longbottom had failed to notice that Neville managed to shift his blankets more snugly over himself moments after birth, assuming that his father had tucked the baby in more securely. Neville's family persistently missed faint signs of magic in him and not until he was eight years old did either his disappointed great aunts and uncles, or the old stickler of a Book, accept that he was truly a wizard, when he survived a fall that should have killed him.
This of course leads to the unfortunate circumstance where a child could actually be magical, but simply be so weakly magical that they are never admitted to Hogwarts. Presumably this is the niche that Kwikspell targets.
It's not clear how this might be different in other parts of the world.
1 From the perspective of the Book of Admittance, anyway; I suspect a parent's expectations would be to assume magical, then gradually change to assume non-magical as no evidence of magical ability presents itself. In addition to what happened to Neville, this is largely what happened to Angus Buchanan, who was assumed to be magical by his parents, and got as far as the Hogwarts Sorting Hat (thanks to deception on the part of his siblings) before being "outed"