From Murat Altinay, a psychologist:

Postmortem studies, which focused on male-to-female transgender brain, found that the brain volumes of transgender women were similar to that of cisgender females in certain areas, such as the central nucleus of the bed stria terminalis or interstitial nuclei of the anterior hypothalamus. These are areas that are essential in sexual behaviors, and the fact that the transgender female brain resembles the cisgender brain was important.

Researchers also looked at some gray-matter volumes and cortical thickness. Again, transgender brains showed similarities to the identified gender even before the patients started hormonal treatment.

Read more: https://consultqd.clevelandclinic.org/the-brain-and-gender-identity-current-evidence-and-implications-for-practice-podcast/

There are differences between the brains of cisgender people and transgender people. Even as a kid, they can feel and suffer from their fate of having their brain in the wrong body. This is not some mere confusion caused by influence. Imagine your brain gets transplanted to a body of your opposite sex. Even a toddler would feel uncomfortable.