Data published by the demographer Carl Haub and Dr. Toshiko Kaneda in How Many People Have Ever Lived on Earth? on the Population Reference Bureau (PRB) website suggests that the 50 billionth person would have been born around 130 AD / CE. This can be seen by looking at the column 'Number Ever Born' in the table below:
Image source: Population Reference Bureau (PRB). Table data sources: Toshiko Kaneda and Genevieve Dupuis, '2017 World Population Data Sheet' (Washington, DC: Population Reference Bureau, 2017); United Nations Population Division, 'World Population Prospects: The 2017 Revision' (New York: United Nations, 2017).
In 130 AD:
- Hadrian was emperor of Rome.
- The Han dynasty ruled in China.
- The Kushan Empire was around 100 years old and had about another 245
years to go.
- Claudius Ptolemy, Greek mathematician, astronomer, geographer
and astrologer, was probably in his 30s.
- Galen, Greek physician, surgeon and philosopher, was an infant
and would have been close to being the 50 billionth person born.
Carl Haub originally made these calculations in 1995 to dispel the myth that
The human population has swelled so much that people alive today
outnumber all those who have ever lived
(His data estimates showed that "those alive in 2002 constituted only about 6 percent", far from the 'myth' of more than half.)
He and Toshiko Kaneda updated the data in 2002 and 2011, conceding that their approach is (of necessity) "semi-scientific". On the methods used in their calculations, the authors say that
calculating the number of people who have ever lived is part science
and part art. No demographic data exist for 99 percent of the span of
human existence. Still, with some assumptions about prehistoric
populations, we can get a rough idea of this historic number...
They take 50,000 BC as the starting date:
Fixing a time when the human race actually came into existence is not
straightforward. Hominids walked the Earth as early as several million
years ago, and various ancestors of Homo sapiens appeared at least as
early as 700,000 B.C. According to the United Nations Determinants and
Consequences of Population Trends, modern Homo sapiens may have
appeared about 50,000 B.C.
This corresponds "to the start of the Upper Paleolithic" and "the emergence of full behavioral modernity" ("behavioral and cognitive traits that distinguishes current Homo sapiens from other anatomically modern humans, hominins, and primates.").
The articles How Many People Have Ever Lived on Earth? and Do Living People Outnumber the Dead? go into details on how the estimates were arrived at (the details are a bit lengthy to include here...).
The margin of error for the birth of the 50 billionth person who ever lived is fairly large; Hadrian may not have been born or Galen may have been dead and buried rather than an infant, but the Kushan empire and the Han dynasty cover considerably longer time periods.