I think my answer here should clear this matter up for you. A couple of other considerations to take into account that I didn't mention are how exactly Octavian could have forged the will, and whether Caesar really intended the adoption of Octavian as a long-term solution. The first is obvious--how on earth can we presume that Octavian would've been able to forge the will? Octavian was a nobody with absolutely no political connections whatsoever. He had nobody who was capable of getting a forged will deposited in the temple of Vesta for him. More importantly, Antony read Caesar's will within days of his death--are we then to suppose that Octavian, who either had not yet heard of Caesar's death or had only just learned of it, had a false will deposited by some political ally that he did not have between the time of Caesar's death (or rather, his learning of Caesar's death) and the reading of Caesar's will? Or, the other option, that Octavian predicted Caesar's death while he was in Spain and had a false will made up and deposited (again, by some non-existent political ally--that absolutely nobody had ever heard of Octavian is obvious from one look at the Philippics) in advance? Both options ring of absurdity. Even if Octavian had somehow deposited a false will, why would Caesar have never heard about it? I was his will after all, and I find it unlikely that its deposition would've been completely unknown to him, that's simply not how Roman law worked.

Additionally, Caesar almost certainly did not expect his death--how could he? Certainly he did not expect it at that time, he was about to leave for Parthia. Gelzer points out that Labienus' defection had a profound effect on Caesar--never again did he place as much trust in a subordinate as he had in Labienus. Antony was given a chance to prove his worth by his governorship of Italy, but he proved to be a complete incompetent, and almost permanently destroyed Caesar's political position in Italy. I agree with those scholars who have suggested that this was, at best, a temporary solution. Caesar found himself without any subordinates competent enough to fill his shoes, and until such time as one could be found Octavian would serve as an adequate substitute--one might suppose, in fact, that Caesar, had he lived, might have groomed Octavian for the office. I presume when you speak of a shared journey you're speaking of Velleius Paterculus' description of Caesar sharing his carriage with Octavian during his campaign in Spain. That's a poorly-attested story from a very minor source--Suetonius (who can hardly, I think, be accused of being an Augustan shill) says that Octavian met Caesar after his ship was wrecked by a storm on his way to Spain, and that he hiked through the Pompeian lines to get to Caesar's camp, which naturally impressed Caesar. Caesar was also a good judge of character, and Octavian's character was nothing if not something that Caesar would've surely approved of.

Rather than presenting the fewest difficulties, it presents the most difficulties if we suppose that Octavian somehow forged Caesar's will. There's really no good reason to think it, and certainly there's no evidence to support it beyond Antony's slanders.

Also, regarding Caesar's wealth, the combination of the loot from Gaul and his victory in the civil war made him by far the wealthiest man in the world. The loot from Gaul alone was enormous--Caesar gives us figures on captives in particular, and the numbers are really quite staggering. Combined with material goods (which Caesar also mentions) and the onerous tax burden which was placed on his provinces Caesar made quite a penny in Gaul--c.f. Pompey's immense wealth after his eastern campaigns.

First off, Caesar had been heavily in debt but after the Gallic wars he had become very rich and no longer so indebted.

Second, Octavian was out of Rome in Greece at the time Caesar died. It is possible that Octavian had an agent forge Caesar's will but it seems highly improbable. Caesar died suddenly and unexpectedly which could not have been foreseen by Octavian. If Octavian did forge his will then he would have been thinking unreasonably far ahead. Caesar was a relatively healthy man prior his death and about to embark on a military campaign. Why would Octavian forge his will when Caesar could be expected to live another 10 or even 20 years?

Moreover, Marc Antony, who would not want to see Caesar's riches go to someone else, was the leader of the Caesarian faction following Caesar's death. Octavian's agent would somehow have had to have reacted quickly enough to Caesar's death to forge a new will and replace the real one, at a time when the will was sure to be under intense scrutiny due to its importance.

Let's also bear in mind that, before Caesar's death, Octavian was just a young insignificant member of the Roman aristocracy. He was not someone with a myriad of spies or other agents at his disposal.

Finally, by the time of Caesar's death Octavian was his closest male relative. As you say he was young and they hadn't spent much time together but Caesar did not have many alternatives within his own family. Modern wills usually bequeath property to family members above all others and the Romans were no different. Additionally, Octavian had impressed Caesar as a young man of ability and potential.

In my view, it is highly unlikely that Octavian forged the will.