It entirely depends on what era you're thinking of. "Greek civilisation" isn't a single monolithic thing: it's possible to trace a kind of continuity from the modern era back to ca. 1400-1500 BCE (so 3400 years ago), but it looks totally different from one millennium to the next. The so-called "Mycenaean" palace culture was 3200-3500 years ago; the so-called "Golden Age" of Athens was 2400 years ago; the reign of the Ptolemies in Egypt was ca. 2300-2050 years ago; the Byzantine Empire, that is to say the Hellenic side of the Roman Empire, came to an end about 550 years ago. Which date you quote will depend on what you're talking about.

Edit: The relevant Wikipedia article will help give some framework, and the AskHistorians book list gives plenty of further reading on ancient Greece.