It is definitely the birthplace of the *term* democracy! And it's probably the first place where there are written records of a state government that considered itself a government by the people. It was also more or less the start of the specific tradition of government that resulted in modern Western democratic institutions, via Rome and then isolated city-state Republics and ideologies that persisted at least pro forma right up until the Enlightenment period.
There were certainly some elements of democracy in earlier literate societies (such as aristocratic assemblies that chose their own leaders), and there were definitely small-scale societies that governed by consensus (probably always have been) but a state that imagined itself as governed by its people *and* wrote it down as far as I know probably did originate with Greece.
There were certainly some elements of democracy in earlier literate societies (such as aristocratic assemblies that chose their own leaders), and there were definitely small-scale societies that governed by consensus (probably always have been) but a state that imagined itself as governed by its people *and* wrote it down as far as I know probably did originate with Greece.