When did humans complete their expansion around the world? I'm convinced, but can't yet prove, that humans first reached the continents of North America, South America, and Australia only very recently, at or near the end of the last Ice Age. Specifically, I'm convinced that they reached North America around 14,000 years ago, South America around 13,500 years ago, and Australia and New Guinea around 46, 000 years ago; and that humans were then responsible for the extinctions of most of the big animals of those continents within a few centuries of those dates; and that scientists will accept this conclusion sooner and less reluctantly for Australia and New Guinea than for North and South America.
Background to my conjecture is that there are now hundreds of thousands of sites with undisputed evidence of human presence dating back to millions of years ago in Africa, Europe, and Asia, but none with even disputed evidence of human presence over 100,000 years ago in the Americas and Australia. In the Americas, undisputed evidence suddenly appears in all the lower 48 U.S. states around 14,000 years ago, at numerous South American sites soon thereafter, and at hundreds of Australian sites between 46,000 and 14,000 years ago. Evidence of most of the former big mammals of those continents—e.g., elephants and lions and giant ground sloths in the Americas, giant kangaroos and one-ton Komodo dragons in Australia—disappears within a few centuries of those dates. The transparent conclusion: people arrived then, quickly filled up those continents, and easily killed off their big animals that had never seen humans and that let humans walk up to them, as Galapagos and Antarctica animals still do today.
But some Australian archaeologists, and many American archaeologists, resist this obvious conclusion, for several reasons. Archaeologists try hard to find convincing earlier sites, because it would be a dramatic discovery. Every year, discoveries of many purportedly older sites are announced, then to be forgotten. As the supporting evidence dissolves or remains disputed, we're now in a steady state of new claims and vanishing old claims, like a hydra constantly sprouting new heads. There are still a few sites known for the Americas with evidence of human butchering of the extinct big animals, and none known for Australia and New Guinea—but one expects to find very few sites anyway, among all the sites of natural deaths for hundreds of thousands of years, if the hunting was all finished locally (because the prey became extinct) within a few decades. American archaeologists are especially persistent in their quest for pre-14,000 sites—perhaps because secured dating requires use of multiple dating techniques (not just radiocarbon), but American archaeologists distrust alternatives to radiocarbon (discovered by U.S. scientists) because the alternative dating techniques were discovered by Australian scientists.
Every year, beginning graduate students in archaeology and paleontology, working in Africa or Europe or Asia, go out and discover undisputed new sites with ancient human presence. Every year, new such discoveries are announced to the other three continents, but none has ever met the requirements of evidence accepted for Africa, Europe, or Asia. The big animals of the latter three continents survive, because they had millions of years to learn fear of human hunters with very slowly evolving skills; most big animals of the former three continents didn't survive, because they had the misfortune that their first encounter with humans was a sudden one, with fully modern skilled hunters.
To me, the case is already proved. How many more decades of unconvincing claims will it take to convince the holdouts among my colleagues? I don't know. It makes better newspaper headlines to report "Wow!! New discovery overturns the established paradigm of American archaeology!!" than to report, "Ho hum, yet another reportedly paradigm-overturning discovery fails to hold up."