What triggers the release of gonadotrophin-releasing hormone with the onset of puberty?
GnRH-secreting neurons are not fully independent. To date, their most studied regulators are kisspeptin-secreting neurons. During childhood, kisspeptin-secreting neurons are off, due to GABAergic higher level structures and to lack of free leptin. So both brain and body fat have a word on it.

Caveat: most of the evidence is circumstantial (for example, higher circulating kisspeptin in naturally occurring precocious puberty) and I am oversimplifying, so the picture is more complex and will become even more so.