Young Sherlock Holmes came out right at the right when I was in the target age group. I thought it was awesome with bacon salt on top.
I can’t think of any other young- things at the moment. Young Frankenstein and Young Guns don’t fit the topic.
Young Einstein? Maybe not, but any excuse to say “Yahoo Serious” is a good one.
One film that might arguably fir here is Young Winston, about Winston Churchill’s early years. But I’ve never seen it.
If you’re looking for treatments of famous figures from long before they were famous, how about the scenes with John Gavin as Young Julius Caesar in Spartacus? The problem, arguably, is that the scenes are wholly imaginary, involving a character (Charles Laughton’s Gracchus) who didn’t even exist (therre were the famous Gracchi brothers, but they were much earlier).
Young Sherlock Holmes was a great ‘curl up with a chick’ movie. For some reason, women liked that movie.