A lot has been preserved, or pieced together from remaining preserved pieces augmented by archaeology; still a lot was lost. So what parts of Greek history or of the culture/phenomena of Ancient Greece, remain unknown or even unknowable?
The most prominent example for a period of ancient Greek history not a lot is known about would be the so-called "Dark Ages" between the collapse of the bronze age civilisations such as the Minoans and Myceneans around 1100 BC and the rise of the Greek polis-states in the Archaic period of around 800-700 BC. At the beginning of this age, the scripts Linear A and B ceased to be used, and writing practically stopped for hundreds of years before the Greek alphabet was created out of the Phoenician script around 800 BC. Therefore, we have very little information about the time in between and the reasons that lead to the demise of the earlier civilisations.
Sources: E. H. Cline: 1177 B.C. The year Civilization collapsed. Princeton 2014; H.-J. Gehrke: Kleine Geschichte der Antike. Munich 2003, pp. 25-28, 39-41. (in German)