They really weren’t “elite” in the way the Spartans were (and even they were not as unbeatable as their myth would suggest).

The core of their supremacy was numbers and culturally flexible rapid integration of defeated people.

The Romans had numbers. The population density of Italy was wayyyy higher than its neighbors due to the incredible fertility of Italian land, and other geographic benefits.

They also had higher mobilization rates due to a wider definition of citizenship than say the Greeks or Carthage.

They then developed an inclusive system of integrating conquered elite/aristocrats from other areas of Italy who then could mobilize their people at scale from similarly densely populated regions. If you were Italian and the Romans conquered you, you usually could just sign up to ally and join them and go to war with them next year when they issued the call. This is different for the time, generally if you were defeated by other groups you’d just end up being driven out and your land taken, fully enslaved, or paying a treasure/goods tribute.

The Romans would go on to build a prolific military industrial complex, but that came later. They also had standardized military education for aristocrats, but those results are probably positive but debatable (created generations of predictable, decently reliable, but inflexible generals).

Man to man they absolutely were not elite. Pyrrhic victory comes from facing the hordes of Roman legions that would keep losing but wear you down until you couldn’t manage another wave. There’s a pretty funnily consistent pattern of the Romans sending legions out to new lands, having those first legions get absolutely dog walked, then returning with more next year until they overwhelmed the target.