C 2100-c 1600 BC
In Mankind and Mother Earth Toynbee writes about the Shang dynasty (c 1500-c 1050 BC) of the Yellow River basin in the second millennium BC as the first historical Chinese dynasty. Nowadays we know more about its antecedents, and we did even by the time Toynbee was writing that book.
The Xia dynasty, the first dynasty to be described in both the Records of the Grand Historian, written by Sima Qian around 100 BC, and the earlier Bamboo Annals had been thought to be a mere invention of the Zhou emperors, who followed the Shang. But excavations from 1959 at an early Bronze-Age site at Yanshi in Henan province – the “Erlitou culture” – have been linked by many (though not all) scholars to Xia. The Xia period would have been c 2100 BC – c 1600 BC.
The Erlitou culture may, in turn, have evolved from the late-Neolithic, pre-Bronze, Longshan culture of the Yellow River (c 3000-1600 BC), known for its (to me) very “civilised-”looking, highly-polished black eggshell pottery. Before the Longshan culture came the early Neolithic Yangshao (c 5000-3000 BC). Toynbee mentions these two Neolithic cultures, but gives them much later dates.
The emperors before Xia mentioned by the historians – the “Three August Ones and Five Emperors” – are certainly legendary.