I am not aware of any ancient societies where the majority of people were atheist, but there certainly have been atheist philosophies that attained some degree of success, for a period of several centuries.
One example is the Carvaka system within Hinduism, which held the following beliefs that we know of:
No life after death, when you die, that's it.
All things happen due to their own nature, and not due to the actions of any god.
Religion is invented by humans, with no divine inspiration.
The Carvaka philosophy apparently originated in the 6th century BC, about the same time as the early Greek philosophers flourished. (Was there contact or communication between them? Some of what is known about their tenets sounds remarkably similar in both groups -- i.e Protagoras, who said "Man is the measure of all things, of things that are that they are, of things that are not that they are not." and "As to the gods, I have no means of knowing either that they exist or do not exist.") It did not completely die out until about the 15th century AD.