I believe the high-school graduation is the "event" where westerners regard the transition from child-to-adult. But that link is not that strong.

There was another way, outlined in the movie Starship Troopers. In that future society, citizenship had to be earned by spending some time in the military. That is definitely worth some consideration, although maybe that right can be earned by other public service vehicles.

In "To My Countrymen", Ben Paine asks the USA for its citizens to pass a simple civics test to get the right to vote. Another idea worthy of consideration.