I disagree with this. The fact that some young prodigies proved it early and eventually became productive adult geniuses is not, to me, evidence that young prodigies will show themselves. Rather, I would expect that there are more young Einsteins who do not receive adequate mentorship, resources, or opportunities to become old Einsteins.
Some make it anyway. Ramanujan is an interesting case. By Hardy's estimate, he was one of the best mathematical minds of the 20th century, and he demonstrated clear mathematical talent by high school age. And he still barely made it, thanks to a fragile chain of people who recognized his talent and drive. It's very easy for me to imagine a world in which Ramanujan stays in India and remains a bureaucrat doing math on the side.
But as I understand it, pedagogy for young Einsteins is still not that well understood.