Athens on its own cannot conquer all of Sicily.
Athens, like other Classical era Greek city-states, has a rather limited hereditary citizen-body, a society which can only support small militia armies for little more than national defence or forcing a rival nation to capitulate. Even with the military aid of allied city-states and colonies in foreign ventures, it would cost a lot to keep the army together. And even the nature of an expeditionary force is ad-hoc. Being made up of citizen volunteers and hired mercenaries, plus the fact that the Strategoi, the army's leadership, are elected to their positions and may not always have a professional background. Even if the Athenian effort was successful, it could not keep the army together to occupy Sicily.
Furthermore, the Sicilian Expedition of 415-13 BCE during the Pelopennesian war was mainly against Syracuse in the eastern part of the island, while the cities of western Sicily were under the hegemony of Carthage, whose supremacy among the other Punic and Greek colonies of the western Med going largely unchallenged in this period.
Athens was not like Rome. Athenian citizenship was mainly hereditary through the patrilineal line. Only rarely did it confer citizenship on individuals for performing a great service for the state. The citizens, rich and poor, were greatly outnumbered by the resident "Metic" population, some of which had lived in the city for generations, and yet couldn't vote in the assemblies or bear arms. While in the Roman Republic, any freeborn individual born within Rome or its colonies, whose' parents were freed slaves, or had roots there, were considered citizens. Plus, communities were sometimes granted either Roman citizenship or granted Jus Latii (Latin Right). This practice of enfranchising their subject states in Italy gave Rome an ever expanding reserve of manpower. States such as Athens just couldn't match up to that.