How old is the Greek goddess Athena?

There really is no answer. If you are trying to say how many years people believed she was real, I have no idea, probably 1,000 to 1,500 years or so. If you are trying to say how many years she has lived since she was born, no one knows when she was born. But Athena is Immortal, like all the other Gods and Goddesses. So long live Athena, Goddess of Wisdom and War.