In order to say when 'civilization' started (or ended, for that matter) you first have to define what you mean by civilization not only by what it IS, but by what it is NOT: what is the difference between 'civilized' and 'non-civilized', and recognize that any such definition will have to be both precise and broad enough to encompass an enormous variety of human societies. Because, almost by definition, Humans are very adaptable, and both adapt to their environment and also adapt the environment to their own purposes. But if you try to use that as the definition of Human (as some have), then you wind up giving the vote to beavers, who adapt the environment around them at least as much as most pre-city-dwelling humans did!
Writing is a poor definer. Non-literary or 'semi-literary' forms of memory are malleable, but amazingly persistent: the tribes of the Pacific Northwest have orally-transmitted stories that accurately describe the flora and fauna at the end of the last ice age in the area - 10,000 years ago. The Lakotah had pictographic 'Winter Count' calendars that accurately recorded events during the year and turned out to be precisely accurate when checked against neighboring literate records from Spanish, French and English speakers. Writing helps, but it is not a requirement for a defined and cohesive multi-generational cultural group.
Technology doesn't work either. Those 'steppe nomads'(Central Asan Pastoralists) actually adopted pastoral herding after starting out as settled river-side hunters-gatherers/herders.fishers and (very primitive) farmers. And as pastoralists, the archeological evidence indicates now that they invented the spoked wheel chariot, the hard saddle for horseback riding, and (possibly independently of other peoples) the composite bow. They also managed to exploit extensive copper, tin and other mineral deposits and produced some of the earliest lost-wax cast copper and bronze objects - a very sophisticate metallurgical technique also invented elsewhere, but possibly later.
In other words, while 'civilization' has been traditionally associated with 'living in a city'. Living in any kind of city (once you find a definition of 'city' - another slippery one) does not appear to be a requirement to have advanced technology, extensive trade, and multi-generational 'collective memories' preserved for longer than written records have been in existence.
Mind you, living in a city surrounded by walls and other people may make it easier for a given individual to be 'civilized', as in having access to the fruits of technology and regular meals, and the benefits of mass population concentrated in cities have proven decisive in the long run, but it took a while: early cities also concentrated infectious diseases, so that they had a net population loss without constant migration of peoples from outside - voluntarily or involuntary, as taking slaves from enemies seems to have been part of every early urban group.
I have a pretty good idea when people started living in cities - the archeology keeps coming up with new finds of city sites, but the trend is pretty clear that people started living in one place in larger-than-individual-family groups about 14,000 - 12,000 years ago (Incipient Jomon, Natufian cultures) and started producing concentrations of 1000 or more unrelated people about 10,000 years ago (Jericho, Tel Qaramel, Motza).
But I'm not so sure that 'living in cities' constitutes the first, or final, or precise definition or indication of 'Civilization', even though the Civ games assume that . . .