One of the main problems that Ancient Greece faced was that, contrary to popular perception, the land quality in Greece was not optimal. Terrain tended to be rocky and grasslands were not common.
Animal husbandry, therefore, was restricted to a small percentage of the population and was not well developed in Greece. Moreover, crops that were grown were resilient, but labor intensive (such as olives) or low in nutrients (for example, barley, as opposed to wheat). During the hot summers, irrigation was necessary, and due to the small number of farm animals, Greeks did not use animal manure or animal power, both of which greatly reduced their agricultural productivity.
All these factor meant that Greece could not achieve the large population that can be seen in large Ancient empires.