I think Athens during the time of Marathon and the Peloponnesian war was around 100,000, not 10,000. I know they sent an army of around 10,000 to Syracuse and after that army suffered disaster, they scraped together another 10,000 and this was after the plague which killed around a third of the population.
Total population of Athens at that time was estimated at
300,000 .
Complete mobilization of all available manpower is usually
set at max of 20% of population giving Athens some
60,000 if all manpower was used.
/bingo
The outlying districts were abandoned in the face of the Spartan advance, and the refugees crowded behind the long wall connecting and protecting the Piraeus and Athens. The population had boomed even before this (Periclean Athens became the marble marvel because of a silver strike on Athenian territory).
Eventually a plague broke out; Thucydides wrote that those infected were incurably thirsty, and crawled into the buried cisterns and water supply culverts, thus spreading the disease to others.
But that plague was early in the war, well before the Syracuse expedition. And the Athenian navy (which was the instrument of empire) required something like 30,000 rowers.