This is not only incorrect, it is completely incorrect.
Gender identity is one of the core backbones of human society. We cannot live without gender identity. Research shows that people who live without their gender identity can die due to the psychological effects caused.
Children identify with a gender because children are eager to learn and children, more than anything, are eager to tie themselves to things that towards what they belong or what they identify with. Children are constantly evolving and trying to form their own identity.
It is not far fetched that a transgender child, after learning the differences between male and female, and socializes with girls, sees themselves as a female. You mention things like trucks and dolls, when that still is impertinent to the subject of gender identity. Some boys like trucks, some like dolls, some girls like trucks, and others like dolls. Yes, society creates a lot of rules of what gender is what, but the whole point of transgender individuals is that they, or rather we, identify with the other gender in terms of physicality (looks, mannerisms, clothes) and in other cases, base interests.