Caesarion was never acknowledged by Caesar as being his son, and there were a lot of Caesarians who refused to believe Cleopatra's claim--in fact, Cleopatra's claim seems not to have been taken particularly seriously or simply was ignored until Antony formally acknowledged Caesarion at the Donations of Alexandria, which was as much a political move to recover his wealth after his failure in Armenia as anything else. That's not to say that Caesarion wasn't Caesar's son--Syme examined the question and I think persuasively argued that at the very least Cleopatra had a good claim, a claim taken seriously enough by the War of Actium for Octavian to really freak out over Caesarion's existence. But it was hardly a sure thing.

More importantly, Caesarion wouldn't even reach his third birthday until several months after Caesar's death. Even if Caesar had acknowledged Caesarion as his son, it would've been foolish for him to entrust leadership of the Caesarians to a three-year-old, especially one with such a strong-willed and politically-motivated mother. Just look what happened to Alexander's son. Not to mention give him the enormous wealth that Octavian inherited from Caesar (and Octavian didn't even get all of the money that was due to him, Antony seized a fair amount of Caesar's estate and refused to hand it over).

EDIT: I almost forgot, Caesarion was legally sole ruler of Egypt, with Cleopatra as his Regent, from 44 onwards, and from birth Cleopatra clearly intended to have him succeed her. Making an important member of a foreign royal family, indeed of a foreign family in general, would've been unthinkable, and the ruler of Egypt no less. Indeed, one of the primary ways with which Octavian turned opinion against Antony was by convincing the Italians that Antony's declaration of Caesarion's parentage meant that Antony intended to have Caesarion take over at Rome, essentially handing over Rome to Egypt. So even if Caesar had lived and changed his will the way he changed it in 45 (which made Octavian heir, not, presumably, Antony) Caesarion never would've inherited