With regard to your first point that black people didn't colonize the world I'll direct you to this article:
7,000-Year-Old Human Bones Suggest New Date for Light-Skin Gene
Black people colonized the world because tens of thousands of years ago there was only black people on this planet. Light skin only evolved 7000 years ago.
It's why there are native black populations in places you wouldn't expect like the Pacific. The humans who went to the Pacific stayed black because their environment was tropical like the one their ancestors left in Africa so they had no reason to evolve different skin or hair. Other early humans who went to areas that were not tropical ended up changing their features to better survive in this new habitats.
With regard to the point about Luzia and the first Americans. Their facial features showed a subnasal prognathism. As I stated earlier this is a feature most commonly seen in "negroid" populations of Sub-Saharan Africa and the Pacific. You don't find subnasal prognathism in Europeans or Asians. If the first Americans were not negroid then they wouldn't have had a noticeable prognathism.
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Non-negroid skulls are typically flat as this old eugenics picture shows. Compare that to the reconstruction and its obvious the first Americans had subnasal prognathism clearly marking their skulls as negroid.
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