He was 25! Augustus started his career at 18 and became 'fully fledged' as the Princeps at 32, if you count it from Actium.
Now if you'd chosen Nero as an example of youth thrust into supreme power I might have agreed with you. A Roman in this age would have been fully mature at 25. He wasn't too young, he was just unsuitable
Augustus achieved his position due to a long and hard struggle with his many enemies (S. Pompius, Antonius, Brutus and Cassius) if he didn't have sharp political instincts he would never survive to his 20th birthday. while Caligula and Nero owned everything they were to the fact they were blood related to the imperial family, they were just spoiled "kids". in respect to his personalty Caligula weren't fit to rule the pseudo-republican system that the empire was.
It's actually interesting but it's seem that most of the emperor who were destined to greatness from birth or younger age turn to be bad emperors while the good emperors actually had to struggle for their position before they came to the throne.