But the idea of living in caves is no longer accepted, docy. Extensive acrhcaeological excavations in Europe have found sites of Paleolithic inhabitations largely in river valleys and other sheltered locations (including alongside large rock overhangs), but to this day there is no demonstrable evidence that Paleolithic peoples of Europe lived in caves.
I myself would agree with your mention of "their own genetic mixture" but would shy away from their being called "a different race" as I see no real purpose for such a distinction. To the former while most Europeans are of the R1a, R1b, I1 or I2 mtDNA haplogroups Native American Indians are of completely different mtDNA groups such as A2, B2, C1, D1 X2a and X2g. Also whereas most of Europe is above 45 degrees north latitude the majority of East Asia, particularly where several NA mitochondrial haplogroups originated, is not. It should also be mentioned that there is a great variety in the skin color of Native Americans themselves.
As a last thought if the Sumerians are related to or descended from members of the Samarran Culture specifically or even to Middle Eastern groups in general, with no evidence to the contrary, then they would belong to the mtDNA haplogroups J1 or J2 and are more likely the latter. There is nothing to suggest they are related to Central Europeans, East Indians nor Native Americans. All of which are modern pseudo-scientific "theories" with no real basis in fact.