This may be more related to anthropology, but:
Just brief readings on Wikipedia indicate that the last migration of people from Old to New World occurred roughly 16,000 years ago, when people still lived in hunter-gatherer societies. This was the status quo for hundreds of thousands of years, prior. The agricultural revolution started only 10,000 years ago in the Middle East, long after these final migrations took place.
How is it that, despite nonexistent communication between the two sides of the globe, people on both sides independently developed civilizations at roughly similar time scales?
Even if you totally discount New World civilizations as lacking in complexity compared to the old world at the time of Spanish (re)discovery of the Americas, these timescales and differences are nearly insignificant when compared to the breadth of time that humans have existed overall.
Has there been any research into this topic? Is there an answer to this kind of question?
As a now deleted comment I assume has pointed out, there's actually a significant time gap between agriculture and urbanism in Eurasia and the Americas. Agriculture in the Near East is dated to at least 10Kya^1 and we see permanent agricultural centered settlements like Catalhoyuk arising shortly afterwards followed by the growth of the complex, stratified, urban settlements of Sumer in the 6th millennium BCE. At the same time Eridu was developing into a nascent city, maize agriculture was only just starting to spread in Mesoamerica^2. It would not be until San Lorenzo in about 1200 BCE that there would be a comparable settlement in the Americas to those that had arose thousands of years earlier in Mesopotamia. Even then, it has been proposed that maize agriculture was still developing and would not be fully productive until around 1000-900 BCE^3. So those are not insignificant gaps and we cannot assume the proximal factors leading to agriculture and urbanism were the same in both areas.
Your question, however, seems more about more overarching factors, and specifically we see multiple loci of agriculture in the Holocene and none before. There actually has been research into this topic. Even taking into account the time humans spent migrating to the various parts of the globe, and the slow, steady growth of human population size, we theoretically still have thousands, if not tens of thousands, of years in which humans could have domesticated plants and animals, then settled down into urban conglomerations. Climate data, however, suggests that the late Pleistocene period in which we see anatomically modern humans was marked by climatic instability. There was considerable fluctuation in glaciation along with temperature and humidity on a global scale at a relatively rapid pace until the advent of the Holocene. Feynman and Ruzmaikin^4, note this climate instability and conclude "there is considerable evidence that climate variability inhibited the development of agriculture until∼ 11,000 ybp when relative climate stability was established."
Richerson et al.^5 also see climate varibility key among several factorcs inhibiting agriculture prior to the Holocene, writing
Probably most important, last-glacial climates were characterized by high amplitude fluctuations on time scales of a decade or less to a millennium. Because agricultural subsistence systems are vulnerable to weather extremes, and because the cultural evolution of subsistence systems making heavy, specialized, use of plant resources occurs relatively slowly, agriculture could not evolve... In contrast to the Pleistocene, stable Holocene climates allowed the evolution of agriculture in vast areas with relatively warm, wet climates, or access to irrigation.
Along with variability, they also note that overall levels of atmospheric CO2 were lower during this period, which would have inhibited the very plant growth necessary for the development of agriculture.
Finally, they observe that there was a period of relative climatic stability during the last interglacial period (130-80Kya) when anatomically modern humans were around. We do not, however, see "behaviorally modern" humans until tens of thousands of years later, as defined by evidence of more complex tools, art forms, living spaces, etc. Their hypothesis is that even if the last interglacial was as stable as the Holocene (and there is some doubt to this), humans were not at a place culturally or socially to develop agriculture.
^(1 Lev-Yadun et al. 2000 The Cradle of Agriculture Science 288[5471])
^(2 Pope et al. 2001 Origin and Environmental Setting of Ancient Agriculture in the Lowlands of Mesoamerica Science 292[5520])
^(3 Arnold 2009 Settlement and subsistence among the Early Formative Gulf Olmec J Archaeological Anthropology 28)
^(4 Feynman and Ruzmaikin 2007 Climate stability and the development of agricultural societies Climatic Change 84[3-4])
^(5 Richerson et al. 2001 Was agriculture impossible during the Pleistocene but mandatory during the Holocene? A climate change hypothesis American Antiquity 66[3])