Some of the answers here are pretty good (although broaden "hormones" to "various proteins including hormones").
Also, parse the question more narrowly. Are we talking about 1 day olds whose hair changes by age six months? Or six month olds who are still tow-heade by who are brunettes by 2?
Or (common) gradually turning from a small amount of blond hair to light brown hair by age four, then darker by age six - and so on?
Developmental genes are involved (and they do produce hormone or hormone-like molecules that affect melanin/pigmentation).
Likewise, some light brown hair (at birth) is subject to quite a bit of lightening by an older age, due to DEpigmentation processes - so that a child can be born with brown hair and end up blondish (especially if their hair is long - and by long, I mean long enough to turn blond, not any particular length of hair).
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