Long term follow up studies prove that kids with gender dysphoria lose it by late adolescence to early adulthood, and they don't want to become transgender adults.
Transitioning a child is wrong, telling them they will most likely grow out of it (the truth) will help them the most.
Here is a link to Singh's dissertation on the topic, with citations and a chart at the very end citing the long term follow up studies which consistently all prove they grow out of it.
It is bad parenting and quackery to suggest transitioning children so young. It is irresponsible to read propaganda for transgenderism to children, it is feeding them false information about what is likely a temporary condition of gender dysphoria.
https://images.nymag.com/images/2/daily/2016/01/SINGH-DISSERTATION.pdf