As some here know, I am a profesional economic historian, and deeply into quantitative data. The last fifty years have indeed seen a move to more reliable quantitative historical data. It started with the prewar international consortium on price history, and in the post war years in France with the group around the French journal Annales, who focussed on the premodern rural history of France, and more. On the demographic side there was the Cambridge Group for the History of Population and Social Structure, doing detailed family reconstitution of mostly 17th and 18th records of births, marriages and deaths. In the US, the biggest methodological revolution was by so called New Economic History scholars like Robert Fogel (Nobel Prize winner) who introduced more advanced econometric techniques and computers to proces and understand large quantities of data on e.g. nineteenth century economic growth, slavery or health. All these projects were hard work, collecting massive quantities of data from the archives. Few of these data series go back very far into time, the earliest ones go back to the thirteenth century, and even those are very patchy, and obviously rely on what was ever recorded, for purposes that were quite different from ours. My own research is on the economic and social history of the Roman Empire, and for that we are increasingly turning to archaeology. With modern heritage legislation archaeology is turning from a field with few data to a field with massive quantities of data. On top of that new scientific techniques such as stable isotope analysis of skeletons that allow us to discover where people were born or what they have eaten in their youth, dna of bacteria in tooth pulp to find out what infectious they were suffering from, or ice cores from Greenland and Antarctica to reconstruct climate and pollution from the deep past, tree rings for climate history, and much more. This is a real revolution, and we are only at the beginning.
The big history of the human race is that of slowly increasing numbers from the neolithic, say from about 12000 BC in the cradle of civilization in the Near East to perhaps 300-500 million in Roman times (see the various estimates published on the excellent Wikipedia page). After that, there was decline and stagnation, until the late medieval world began to see some growth again, and exploding with the Industrial Revolution. With some delay, we not only became more numerous, but also more prosperous, and that prosperity growth has continued and expanded across the globe until now. This is in sharp contrast to the world before the Industrial Revolution when population growth usually depressed standard of living: labour became more abundant and hence cheaper, and land became increasingly scarce, and hence commanded higher rents. From time to time this was followed by a Malthusian check such as famine or a pandemic like the Black Death (also preceeded in turn by a rapid deterioration of the climate), which reduced population (and indeed sometimes by half), making labour scarce and expensive, and land abundant and hence cheap. So changes in the the functional distribution of income went hand in hand with changes in the social distribution of income. The only preindustrial exceptions to this viciuos cycle were the Netherlands and England from the sixteenth century where real wages were about twice as high as elsewhere. This provided an obvious incentive to technical innovation, and in the UK this ultimately led to the Industrial Revolution, which marks the sudden increase in population due to the decline in mortality from infectious disease (before that life expectancy at birth had been in the 20-35 years) due to public health measures, and not yet followed by a decline in natality, and the increased productivity from new technology that slowly began to improve incomes even though population also increased (the escape from Malthus).
This is of course a very crude summary, and a lot of research is going on to find new data, or proxy data for earlier periods. I am currently working on a big project with a dataset of 10000 skeletons for the Roman period, to chart changes over time in body length as a proxy for health (first publication in Economics and Human Biology). Body length is a prominently researched indicator of more modern population health (mind you, not for individuals), and provides an extension of the concept of standard of living beyond money income. We are trying to move this into earlier history, and hence with skeletal data rather than e.g. military archives, but the methodological challenges are for real. Climate history poses similar challenges, and Kyle Harper's recent College de France lectures are a good showcase of current thinking (online, but in French).