There's no proof gender identity even exists, nevermind that it's innate. The whole idea of 'gender identity' rests on Man-made stereotypes of male and female behaviour, dress, roles etc. Without those stereotypes there's nothing to transition to.
If two babies, one male one female, were shipwrecked on an island and miraculously lived until adulthood, how would they know their 'innate' gender identity? Without stereotypes of male and female dress and behaviour around them to refer to what would be their frame of reference for having say a 'male' gender identity? Their sex would be male and female and they would likely know their sexuality, but how can gender identity be innate when it can't exist without reference to already the long established regressive stereotypes of what 'man' and 'woman' means?
There's no evidence, as far as I know, that elderly gay people with dementia forget they are gay. There does seem to be some evidence that elderly transgender people forget they have transitioned. Why would that happen if gender identity is innate?
https://www.google.com/amp/s/www.bbc.com/news/uk-wales-43365446.amp