Octavian and Antony probably didn't know each other before Caesar's death, and at most they only met once or twice. Suetonius says that Octavian first met Caesar during his Iberian campaign, in 45, when the ship carrying Octavian to Iberia (where he was to serve as a minor member of Caesar's staff) was shipwrecked and Octavian walked through the enemy lines to Caesar's camp, a feat which Suetonius says impressed Caesar. One would expect it might be likely that Antony and Octavian would meet during that campaign, except that Antony, having been completely disgraced during his governorship of Italy in 47 and subsequently alienated from Caesar, remained in Italy during Caesar's campaigns in Africa and Iberia, so he couldn't possibly have met Octavian during that time. We have no indication of whether Octavian stopped in Italy after the Iberian campaign, but it is much more likely that he just proceeded straight on to Illyricum, where he began the military training which he would still be undergoing in 44 when word was brought to him of Caesar's death.

It's important to note that everybody expected Antony to be Caesar's heir. It's almost certain that Antony was Caesar's original heir by his first will, but Caesar's revised will, deposited with the Vestal Virgins in September of 45 (immediately after returning from Iberia), seems to have countermanded that. In Caesar's revised will it was Octavian who inherited two-thirds of Caesar's estate and fortune, as well as Caesar's name and the loyalty of the legions. Much of Antony's actions just after the conspiracy can be readily explained by an expectation that he would inherit, and it came as a shock to everyone when Caesar's will was read that it was Octavian, a nobody, who would get everything. Antony had been quite firmly pushed aside by Caesar after completely fucking up his governorship of Italy, but Caesar had revised his will secretly and so nobody knew that there were any changes in it--it was quite common knowledge before that Antony would almost certainly inherit. Not surprisingly, Antony chose to ignore the will, acting essentially as dictator in Caesar's place. When Octavian arrived in Rome later that year (mind you, Octavian at first was only told that Caesar had been killed, and didn't learn the contents of the will until he was actually in Italy--he decided to return, despite the danger of assassination by Republicans for his connection to Caesar, to see if he could get any inheritance or use the confusion to begin building a political career) Antony refused to hand over Caesar's fortune and violently opposed Octavian, bad-mouthing him in the senate. Octavian's political maneuvering is quite impressive--unlike Antony, who managed to piss off Caesarians and Republicans alike, Octavian played both sides of the fence marvelously, winning over both prominent Republicans and stealing important Caesarians (including, illegally, since he held no magistracy, commanding an ever-growing number of Caesarian legions, defected from Antony). Importantly, Octavian won over Cicero to his side. Cicero was Antony's arch-enemy, the man who delivered the scathing Philippics, and when Octavian promised that he could get rid of Antony Cicero readily agreed. The turning point was when Antony stormed off to Cisalpine Gaul late in 44 and besieged Decimus Brutus at Mutina. At the beginning of 43 the senate enrolled Octavian as a senator, and immediately voted him an extraordinary magistracy (which gave him legal control of the illegal army he had already built up of defected Caesarians) with the mandate to assist the consuls Hirtius and Pansa in destroying Antony. In the ensuing battle Antony was defeated, but both consuls were killed, and Cicero was able to get the senate to grant Octavian consular powers to his extraordinary magistracy. In a brilliant coup Octavian suddenly turned on the senate, camping his Caesarian and consular legions in Cisalpine Gaul and eventually joining forces with Antony. During the next couple months Octavian made a fool of the senatorial faction, allying himself with Lepidus, a supporter of Antony and one of Caesar's most trusted lieutenants, and demanding the vacant consulship from the senate as well as a full pardon for Antony. Around the same time Antony and Lepidus met with Octavian to discuss a political alliance, and by October Octavian (who had been made co-consul in August) proposed a bill that was passed by the comitia that formed the Triumvirate