It depends on what you want to consider a democracy. Even before the Greek cities the most basic form of government for a village was a council led by the elders where the community can discuss the developments of its politics, at least for the rightful political subjects recognized by that community. This is anyway not democracy as we can think of now, if you think about that it's the prototype of every possible form of government that is born after the prehistoric age, as you can have forms of monarchy, oligarchy, dictatorship or democracy born by similar conditions. More so in ancient and medieval times no political leader was completely entitled with absolute power, every king usually must refer at least to a council of nobles or notables from his reign if not at some comunal parliament from all around his country (at least for financial matters ). No dictator was assumed to ignore the will of his community that usually would state limits and temporal extent of his dictatorship. Even the Roman emperor has to consider the humors of the Empire to stay in charge more than a season, squeezed between Senate, Pretorians, the different armies of the empire and the ruthless population scattered all around the roman sphere of influence. On the other hand not even the Greek model was an example of a modern democracy, and even if it presented openings on a larger scale of population (at least in Athens ) still managed to exclude from the political activities many subjects like women, immigrants and people with no property. So, what do you mean for democracy? A council of people of the same place talking about matters of their own community?

I had a similar question regarding voting - Did anyone besides the Greeks independently come up with the idea of voting?. My idea was that democracy's most defining characteristic is the counting of votes (as opposed to simply debating/persuading + voting by acclamation). You can see the discussion there.

Athens wasn't a democracy. Only about 5000 Athenians had political rights (classified as citizens) the majority of the inhabitants, including masses of slaves of course, had no political or legal rights at all, and of course only men could vote.