You could call him a teen or a teenager, if the protagonist thinks from his appearance that he is over 13 and under 20, but doesn't know if he is a legal adult or a legal minor.
You could look up definitions and synonyms of "boy" and "man" to find words which are synonyms of both.
Here is a link to about two dozen synonyms for boy:
And here is a link to a list of synonyms for man:
Words which are on both lists include fellow, and guy. Other lists may have more words used for both "boy" and "man".
If the protagonists dislikes him a first sight she might think of him as a "jerk". If she thinks he is really good looking she might think of him as a "hunk" or a "dreamboat" or other slang term with the same meaning.
Maybe she thinks of him as a 'boy" sometimes and a "man" other times.
I note that in Star Trek: The Original Series the main characters who were in their thirties and forties sometimes called other adult characters "boys" or "girls". They called several adult women "girls", and in "Shore Leave" Yeoman Tonia Barrows calls herself a "girl" at least once, despite the actress being 33 years and 9 months old when her scenes were filmed. In "Balance of Terror" Dr. McCoy calls Lt. Robert Tomlinson a "boy" despite him being portrayed by an actor 26 years old.