Quite a few aspirations can be completed while your heir is a teen. Renaissance Sim and Computer Whiz can both be completed within a couple of days of becoming a young adult. Those are probably the aspirations you want to focus on first. Then, as MarianT says, use some of the longer aspirations as shared aspirations for farming points. Also, remember that your heir cannot switch aspirations until they complete their unique one, so you probably want to get that done as soon as possible.
There are even things you can work on while the heir is a child, like collecting frogs toward the completed collection for Curator, catching fish to meet the "Collect 20 types of fish" for Angling Ace, Logic skill for Renaissance Sim/Nerd Brain, and violin or piano for Musical Genius, etc. If you know they'll be going for Computer Whiz, have them spend a lot of time on the computer playing the math game or practicing typing/playing Keyboard Commander so you get those 100 hours in early. Once they max Mental, they can start getting Video Gaming skill, too.
