Which early civilization had a republican form of government for part of its existence?

There are two civilizations that might fit this answer.

The first is Ancient Greece, that is Athens. Athens had a democratic government that resembled a republican one but since they were only a city-state and not a huge republic then historians are wary when they talk about it in terms of republicanism. They did however have a democratic government with an elected senate and suffrage rights.

The second is Ancient Rome. Up until Augustus became the emperor and turned it into the Roman Empire, Rome was a republic. They were a republic in the true sense because they had the senate which would vote for new legislation and this covered the entire Roman republic which was huge, not just the city of Rome.