Yes. Many transgender people know from a very early age that their internal gender is not the same as the gender they were assigned at birth. Some are very vocal about it as young children as early as age 5, others take more time to understand their gender identity and communicate it to others. For many, cultural expectations and norms make the process more difficult and complex.

If you know a transgender or gender non-conforming child, and would like to learn more about how to best support them here are some good resources:

American Academy of Pediatrics 
Gender Spectrum
Gender Diversity