What if Octavius never traveled to Hispania? Caesar may well have still adopted his nephew in order to make him his beneficiary. What would have happened if there were no Octavius? Possibly Marcus Antonius would have consolidated power.
Would we have no transistors today if Shockley hadn't worked at Bell Labs?
I guess my viewpoint strongly biases me towards seeing continuity and underlying processes. For every tipping point, there was a pre-existing process; for every process an event you can treat as a "handle".
They were all hyper-ambitious patricians. The conservatives (optimates -- the best) regarded the populares (the faction Caesar aligned himself with) as people willing to threaten the order of the state by pandering to the masses. This is what Catiline did, and Caesar too. This was the basic threat that the Gracchi brothers appeared to present in agitating for land reform and something that underscored Caesar's political agenda (he had to find land for his loyal veterans).
Julius' murder two years later on 15 March 44BC resulted in Octavian traveling to Rome to claim his inheritance, winning the loyalty of much of the army in the ensuing chaos, defeating and executing a number of heavy hitters including Mark Antony, Cleopatra, and Caesarion (Julius' son with Cleopatra), and eventually becoming the first Roman Emperor.