OK, no significant example before our time. Granted. But in our time, over the recent several decades, there have been already several examples of societies maintaining moral life without the aid of religion, in that the majority of people in these societies do not actually believe in god or gods or any religion. The main examples are Czechia, Estonia, and the Scandinavian countries. It is true that a majority of people in Scandinavian countries call themselves Lutheran, but then most do things like infant baptism and Christmas more as a custom, a tradition, more like an ethnic tradition, rather than for any reason of faith, since as far as faith, they are mostly atheist or agnostic. So for them calling themselves Lutheran is really a matter of tradition rather than belief. Few are believing Lutherans. Few go to church often. Yet these countries have a far lower rate of murder or other violent crime than here in the US, where most are believing Christians. So most Czechs, Estonians, Swedes, Danes, Finns, Norwegians, Icelanders and Faeroese maintain quite a moral life without the aid of religion. Though I think nobody is perfect, there is nobody who has never done anything in his or her life immoral. And my opinion agrees here with the Jewish Bible, so this is the usual Jewish opinion. Of course Christians believe in one exception, Jesus. And some Christians believe in another exception, his mother Mary. And some Christians also teach that little children, below the age of accountability, are considered sinless.
In Czechia, the mostly impoverished Roma minority has a considerably higher rate of crimes than the Czech majority, even though a considerably larger percentage of the Roma (traditionally called Gypsies) are believers in a religion than Czechs. In Estonia, the Russian minority has a higher rate of crimes than the Estonian majority, even though a higher percentage of Russians are believers. In Scandinavian countries like Sweden, Norway, the Muslim minority has a considerably larger crime rate than the local Scandinavian majority, even though most Muslims are believers. Though I am certainly not saying religion causes crime. There are specific sociological reasons for each of these minorities of why they have higher crime rates.