Some kids do know from pretty early on that their bodies are not doing what a boy's or girl's body is "supposed" to be doing. This is particularly true if there's a more obvious underlying cause driving this - intersex genes, something up with their gene expression, etc.
And it can cause quite a lot of distress if there's nobody around to say "hey, it's ok, there's a word for this and it's transgender." Suicides related to this can happen in kids as young as 8 or 9. And to be frankly practical, if we can't agree that a kid shot up on hormones HAS to be better than a dead kid by suicide, then I'm done with the human race entirely.
So, again, try to get away from this idea that transgenderism is a choice in the vein of some kind of arbitrary whim. It might seem odd to you that someone at six years old can just know that something's not right, but that may well be because you didn't live through the experience of a six year old where something isn't right with what they've been told about their gender. (And nor did I, for that matter. I do wish this site were less hostile to the trans community because we should be learning all this directly from their experiences.)