If the first humans were black, then moved to colder environments, then why do black people have white skin on the bottom of their hands?
Because it doesn't get sun exposure.
My compete guess is that the region of skin where the colour is expressed mostly follows the same region as for hair follicles. So not palms, the bottom of the feet or stuff that goes inside.
And their feet. Lack of regular intensive sun exposure on the palms and soles.
Most mammals have light skin that is covered by fur, and biologists believe that early human ancestors started out this way also. Dark skin probably evolved after humans lost their body fur, because the naked skin was vulnerable to the strong UV radiation as explained in the Out of Africa hypothesis.