Why doesn't the Chinese language have a one character word for "young"? There are one-character words for "old", "love," "book," and many more important concepts. Why is 青年 the way to say "young" and not a one-word character?
It does. 少 means young. See 少不更事

There are also 幼 for children and 老 for old( you already know).
孟子 said: 老吾老以及人之老,幼吾幼以及人之幼