Here's a little breakdown of how most people refer to these phases of the Roman republic.
The Early Republic (500~275BC) - Starting at the founding of republican government, ending when Rome overcame Pyrrhus and shifted its focus to Carthage. This period saw Rome struggle for survival before struggling for dominance and the difficult position it found itself in forced Roman people and leaders to be flexible, opportunistic and resilient, or capitulate. By the end of this period, the Romans controlled a dominant part of the peninsula, binding former enemies to themselves through patronage.
@IGdood the Camillan reforms took place smack dab in the middle of this period, sometime after Brennus' sack of Rome.
The Mid Republic (275~150BC) - This period is defined by the three Punic Wars, though the Romans were often fighting in many places simultaneously. Ending with the destruction of Carthage, the strained political institutions of the republic, originally designed to meet the needs of a small Italic city-state, were strained in trying to manage Rome's massive expansion from Spain to Africa to the Aegean.
@torongill - I see your point, but those battles were not small and the number of soldiers we think actually fought in them still dwarf what TW is able to represent on screen. Just as some of the first battles in S2 and other TW titles are smaller, so would be those for Rome in an early republic start - not a bad thing to start small.
@Rhaegar - It sounds like you're worried that, by the late game, factions which were historically relevant might not be powerful, or even present. I think that's a good thing!
TW does not recreate history, it reimagines it, and it's fun

If a player (or AI) wants to develop a pastoral Celtic society into a cosmopolitan coastal city-based people with professional armies, well that should be achievable.
CA's job is to balance that reimagining such that it develops in authentic ways.. but the process is subjective and they can't please everyone. But imo, if one of Alexander's successor states has crushed the others by late game to create a new, massive Eastern empire, that's not bad.