I'm not sure I understand your question, are you asking 'how could Athens afford something as grand as the Parthenon if it was just a city-state?'

In the aftermath of the failed Persian invasion of Greece, there were two major Greek powers: Athens and Sparta. The latter, after defeating the Persians were uninterested in continuing the war into the eastern Mediterranean. Athens then took up leadership of a collection of city-states, many in the islands, and created the Delian League - named after the island of Delos where the treasury of the league was. The league then proceeded to take the war to the Persians in Ionia and liberate other islands from Persian control.

Over time, Athens began to treat the league less as a self-defence force that they were the leading voice in to their personal empire. The league treasury was transferred from Delos to Athens and the funds used to rebuild the city and build the Parthenon on the justification that Athens had been burned because of its refusal to submit to the Persians during the Persian War.