Gigantopithecus as well as many hominins besides Homo sapiens, did evolve and radiate across Asia?
Homo Erectus/Heidelburgensis/Neanderthals/Denisovans were all widely distributed outside of Africa. Neanderthals and Denisovans in particular have no records of ever having their range include Africa (Neaderthals may have lived in parts of North Africa but they’re firmly Eurasian). Homo Floresensis only ever lived in Flores.
Gigantopithecus, a giant non-hominin Ape, only has evidence of living in China. It’s thought to be related to Orangutans. You probably are dismissive of Orangutans because they are only a single ape (actually multiple species) outside of Africa in the present day but the Ponginae subfamily including Orangutans and Gigantopithecus had many other species, they are just now all extinct, but all were Asian: https://en.m.wikipedia.org/wiki/Ponginae
That said, I do think there is no evidence that Homo Sapiens “evolved outside of Africa” and I suspect most people who do push this are doing so for either nationalistic reasons (we found early hominin fossils in our country, we must be where humans evolved and are the “original” humans!) or racism (not wanting to be descended from “Africans”). But it’s definitely possible there was gene flow from Homo Erectus outside of Africa back into Africa in a way that made it into the human genome, and many people have non-African human ancestry from Neanderthals and Denisovans