The genetics of Andaman Islanders (off the coast of Burma), together with paleoclimate data, pretty strongly suggest that they were isolated from other human populations for about 20,000 years and fit more or less within a range of genetic variation that still exists today in Northeast India. Only a handful of human populations have been isolated that long, and most have seen massive waves of population replacement, sometimes multiple times, since the introduction of agriculture.
The observation that the only population in Europe that doesn't speak an Indo-European or Uralic language, the Basque, are the most lactose tolerant population in the world (suggesting their ethnogenesis probably took place sometime after a selective effect that arose after the development of dairy farming allowed the trait to reach fixation in this population), likewise dispells the notion that any large current population of Europe draws much of its ancestry from Upper Paleolithic Europeans.
Only a handful of modern populations have a strong likelihood of having more or less uninterrupted descent from the pre-Last Glacial Maximum populations of the places that they live today. For example, pre-LGM (ca. 20,000 years ago), the Americas and much of Oceania were uninhabited. Most, but probably not all, Tibetans have genetic origins in East Asia at sometime since the LGM.
The Bantu populations of Southern and Eastern Africa are more recent arrivals, as is the population of Madagascar. Before then, Southern Africans looked like modern Bushmen, they weren't racially the same as what we now call "black" Africans. And, Africa's West Africans and Nilo-Saharans are likewise populations that are probably predominantly products of migrations and population expansions within the last 20,000 years.
There are very strong indications from multiple lines of evidence that all modern humans have common origins in a single human community within the last 250,000 years or so somewhere in Africa, and the similarly strong indications that all non-Africans probably have origins in one (or at most two or three) main migration events sometime in the last 100,000 years. But, we can draw only weak conclusions about the first 80,000 years of our existence as Eurasian hunters and gatherers from the genetic landscape of today. Indeed, it is extremly challenging simply to discern the outlines of the first 7,500 years of our pre-history from the time that agriculture and domesticated animals other than dogs arose until written records began to recount events with any regularity.
The latest discoveries from ancient DNA and archaeology and population genetics increasingly suggest that in Europe, at least, there isn't even all that much genetic continuity between the early Neolithic era and the present. In most of Europe, there have been at least one or two major waves of population near replacement since then. Large swaths of Europe have their genetic roots predominantly in Indo-European migrations and expansions that have taken place since the Bronze Age (in other words, since about 2,500 BCE).
Of course, in some places, the current population traces its roots where it lives now much less far in the past. The vast majority of North Americans predominantly have ancestors who arrived in the North America within the last five hundred years, and the median ancestor of a contemporary North American probably arrived within the last century and a half or so. Northern Thailand experience a major population replacement in the 13th century. Northern Japan experienced a major demographic shift in the last thousand years, with Hokkaido experiencing that shift in the last few hundred years. New Zealand has only been inhabited for about a thousand years and has experienced 80% to 90% population replacement in the last couple of centuries. Population replacement was even more complete in the last couple of centuries in Australia. Texas, California and much of the rest of the Western United States have gone from being populated almost entirely by people of Iberian and Native American descent in 1800, to being populated predominantly by people descended from neither of those populations today. Jews were a tiny proportion of the population of Israel a century ago. Most of the Han Chinese people in Western China have roots there only in the last seventy years, and most of the Caucasians in Eastern Russia have roots there within the last two centuries. The white and colored populations of Southern Africa didn't exist when Columbus sailed across the Atlantic. Large shares of the population in Kuwait and Saudi Arabia and the United Arab Emirates are non-citizen foreign workers. The vast majority of Alaskans have roots there only in the last seventy years.
While Young Earth Creationists are profoundly wrong about the age of our world, of our species and our life on earth, most of our cultural legacies can be traced to the Holocene era, which starts roughly when the Young Earth Creationists claim that the world came into being. The most widely accepted estimate for the origin of the Indo-European language family that includes languages from Gaelic to English to Greek to Persian to Hindi is about 6,000 years give or take a few centuries. Sumerian, the most widely spoken language of Iraq and the first to be recorded in writing, is a dead language, as are all other languages that can be definitely said to belong to the same language family. The pygmy languages probably died sometime in the Bantu expansion. The languages spoken in Pakistan's civilization for thousands of years prior to the arrival of Indo-European languages are probably lost and completely dead now. The Afro-Asiatic languages that are still spoken today probably have a common origin no older than farming, and Arabic, the overwhelmingly dominant member of the linguistic macro-family was spoken by no one but some minor tribes of herders in the Arabian desert as recently as sixteen hundred years ago. Twenty-five hundred years ago, no one in Japan spoke Japanese. Two thousand years ago, no one in Turkey spoke any language even remotely related to Turkish.
The oldest of the world's major organized religions that is still practiced today, Hinduism, is probably about 4,500 years old. Polytheistic religions that were dominant from England to Egypt to Finland just two thousand years ago have only a tiny number of practioners and most of those practitioners are neo-pagans are who resurrected those faiths after more than a millenium in which those faiths had vanished from old myths and images starting in the 18th or 19th century.
Foods that now define nations, like potatoes in Ireland, spicy kim-chee in Korea, and black tea in England were never consumed in those respective countries five hundred years ago. Bananas never found their way into the diet of African monkeys until human mariners brought them there around the time of the Bantu expansion or later. The Kumara that is central to the Maori diet in New Zealand and in much of the rest of Oceania somehow made its way from South America (probably in a single sea voyage) in roughly the last millenium.
While we have approximately 5500 years of written history for at least parts of the world, mass produced books are only 500 years old.
Modern political and economic institutions are even younger. There is no place on earth that has been continously a democracy for a thousand years. All but a few of the world's democracies were democratic two hundred and fifty years ago, and even in those places the franchise was much narrower than it is today. Two hundred years ago there was almost no where in the world that women were allowed to vote. When I was born, about 95% of law students were men, now it is just over 50%. All but a few of the current regimes in Europe have been interrupted in the last seventy years. Slavery has gone from being an international norm to an abberation in two hundred years. The use of the death penalty has declined dramatically in the last two or three generations. Marriages that aren't arranged have been the norm for less than a couple of centuries in most of the world, and in many places less than a century.
We are becoming aware of our most ancient roots just as the last traces of them are vanishing.