It seems likely that (as a rule) genius is inborn - and the way this works could be described in terms of an acorn which grows into an oak.
The pre-requisites of genius are intelligence, which we know is mostly inherited; and creativity, which is much less well understood, but which is also substantially in-built.
(Intelligence cannot be taught, although IQ tests can - neither can real creativity be taught.)
So a mature, adult genius is a product of the growth and development of a child in whom the ingredients and their balance can be traced right back to early childhood; much as the oak tree grows from the acorn.
So, there is destiny to genius - and the primary qualities are either absent, or present (to varying degrees) from the very start - and (unless thwarted) these qualities will tend to unfold by their own inner logic.
And as with an oak tree, the exact, specific result depends on the environment - if the tree is growing in thin soil on the top of a windy mountain, the tree will be stunted and bent; if alone in the middle of a landscaped park it may grow to symmetrical magnificence.
But, whatever the final result - even if the oak is eaten as a sapling by a rabbit - its basic potentiality and distinctive nature was in the acorn from the beginning.
Note: The acorn metaphor (although not my proposed psychological mechanism) comes from The Soul's Code by James Hillman (1997), who also collected a wide range of examples.