Spartan aversion to money probably dates to after the Peloponnesian War, but in any case, Spartan pre-eminence was not based on money.

To start with the first point: all Spartan laws were attributed to the mythical lawgiver Lykourgos, who supposedly lived in the distant, ill-defined past, and created the Spartan state in its perfect and final form. However, if we compare different accounts of Spartan life and customs, we can clearly see that some of the laws later attached to Lykourgos were not actually in effect throughout Spartan history. The Spartans apparently found it convenient to claim that every law derived from Lykourgos, even if they had only just enacted it. We should not be distracted by the claim that Lykourgos decreed this or that law; it is far more important to see when that custom actually appears in sources on Sparta.

In his groundbreaking Property and Wealth in Classical Sparta (2000), Stephen Hodkinson shows that the ideal of extreme austerity and the ban on money does not occur in any account of Spartan life before the 4th century BC. Indeed, in Herodotos and other sources, Spartans are shown happily taking bribes, which wouldn't make sense if they were not allowed to own money and if there were no ways to show off one's wealth in Sparta. While it's true that Sparta didn't mint its own coins until the 3rd century BC, there seems to be no reason to assume that their attitude to money was very different from that of other Greeks at the time of the Peloponnesian War.

In fact, ever since Aristotle, scholars have argued that the reactionary Spartan attitude to coined money was because of the Peloponnesian War. Their final victory and capture of Athens brought immense quantities of money into Sparta, destabilising their internal politics and awakening ambitions in prominent Spartans that were regarded as dangerous. It was only in response to this vast influx of cash that the Spartans outlawed money - inevitably justifying the move by claiming that this went right back to Lykourgos and had always been the Spartan way.

This is not to say, though, that Sparta was always awash with coin. There was no formal tax system that we know of, so that the wealth of individual Spartans did not result in a large treasury. According to Thucydides, at the start of the Peloponnesian war, both sides were well aware that Sparta had no accumulated reserves of money, which limited their ability to wage war at a distance or for a long time. Their success in war, therefore, was based on other things - which brings me to my second point.

Spartan power was based in the 2 great resources of the Archaic period: land and men. After the conquest of Messenia, they had the largest territory of any Greek state. At its peak, they probably had about 9,000 citizens, all of whom were members of the leisure class who could afford to equip themselves as hoplites. This made Sparta the local big dog, and in the course of the 6th century BC they subdued their neighbours one by one. After some setbacks against Tegea, they decided to abandon the notion of subjecting defeated enemies to helotage, and instead began to incorporate them into the unequal alliance system we call the Peloponnesian League. Members of the League were required to fight on Sparta's side, meaning that every conquest increased the Spartan army, while no individual state had the power to defy Sparta's commands. By the 490s, even Sparta's great rival Argos was crushed, and Sparta controlled the entire Peloponnese.

Levied from all the members of the League, the Spartan coalition army wasn't a standing force paid from the state treasury, but a militia obliged to follow wherever Sparta led. In theory, it required no money to bring this army into the field. By the 5th century BC, it seems to have become normal to compensate Greek militias for their service with a daily wage, but for this Sparta could simply demand "contributions" from the members of the League, so that they ended up paying for their own service. This meant that, despite the outward poverty of the Spartan state, Sparta was able to field the most powerful army in the Greek world.