Uhhh, sort of, but not really. Octavian was enrolled into the senate at Cicero's urging without having held any senatorial magistracy early in 43 when he was still 19. Theoretically you were supposed to not be eligible for the quaestorship, and thus the senate, for like another 10 years--special enrollments were far from unknown, however, and really pretty common after Caesar got back from the civil war. What is unusual is that he was granted extraordinary imperium. This was essentially a recognition, really, of the already considerable private army that he illegally held, and an attempt by Cicero to firmly adhere it to the state. Private citizens with illegal armies being granted imperium were not totally unknown, nor was it unprecedented that they individuals might be quite young--Pompey was 23 when he recruited three legions at Pisenum as a private citizen--but it was still unusual. Octavian's unprecedented power, however, that resulted in his appointment to the consulship late in 43, was largely accidental. The deaths of the consuls Hirtius and Pansa, to whom he was subordinate, in battle had left him with a force several times larger, and in a stroke of extreme good fortune the consuls had been victorious, allowing Octavian the leeway to both negotiate with Antony and threaten the city without fear of serious attack to his rear. It's easy to imagine this rather fortuitous string of circumstances going a totally different way.

Individuals of extreme power had risen previously both at a young age and through extraordinary avenues. The greatest example was Pompey. We've already seen that at only 23 Pompey had raised a private army and two years later he was in Sicily with a propraetorian commission to root out anti-Sullans--attaching himself to Sulla both politically and legally (he married Sulla's stepdaughter probably by or before 82) allowed Pompey all kinds of avenues for rapid unorthodox advancement. By the time of Pompey's (illegal, he was not old enough nor was he yet a member of the senate) triple triumph at 27 he had power equal or even greater to Octavian's, though he didn't immediately convert it into a consulship the way Octavian did--Octavian was somewhat helped by the fact that in his case the dictator was dead and the state in disarray, whereas Sulla was still very much alive and kicking when Pompey was climbing the ladder. Like Octavian Pompey was appointed to the consulship without having ever held electoral office (he was the first to do so)--Pompey did it in 70, though, at the age of 36. Pompey probably could have gotten the consulship earlier but was more interested in fighting wars in Spain and against Spartacus following his triumph. So in that respect Octavian's actual legal power certainly far surpassed Pompey's, although Pompey's power as a young man was certainly comparable, even if he didn't immediately convert it into magistracies the way Octavian did