The chain of events leading to the specific civil war that ended the Republic started much earlier, and included several earlier civil conflicts. You can look for "the beginning" of this chain of events in a lot of places, but probably the easiest to grasp and most direct precursor was the Gracchi brothers' efforts to empower the plebs, which created two opposing political parties; followed by Marius' reforms loosening restrictions on army enlistment, which had the consequence of making soldiers beholden to their commanding general rather than Rome as a whole; followed by Sulla's dictatorship, which set a precedent for a strong general controlling things in an ostensibly Republican form of government.

Pompey and Caesar grew up under Sulla's influence. Alesia, while enhancing Caesar's profile, isn't any more of a precursor of the civil war than Pompey's big victories.

I wouldn't classify it so strongly, but it can be seen as such a seminal moment in Rome's history because it represented an end to the Gallic threat. The Gauls had sacked Rome hundreds of years earlier, and had always presented the big, bad, scary barbarian threat (a role that Germanic peoples would later fill).