I mean at the start of the story the it's the FL that develops feelings for the older guy and the older guy starts treating her as his little sister, which I think because not only was she 13 but she was his friend's little sister, which I think can be normal in Asian countries or even Western countries for a little girl to like older boys or even young adult men since they think they are more mature and cooler than the boys around their own age group or something like that. But then I think they would usually grow out of that feeling (e.g. Japanese tropes/clichés in manga and other media of a little girl saying she wants to marry her father or older brother when she grows up, I think some other Asian countries might have this too).
There are also 2 time skips in the story later if that makes you feel any better lol, 1 when she becomes a high school student and then they do another time skip literally right after to when she becomes a college student, so the guy wasn't trying to pursue a 13 year old when he was 20
Not trying to justify relationships of a guy that is 18+ year old having romantic feelings for a minor that is well below the legal age (i.e. a 20 year old and a 13 year old which is the case of this story I think) because that's weird, but just trying to explain the rationale of this story.
This is very lovely story. Most great part about the story is how the author handled the age difference part without giving any creep vipe... without giving a spoiler I can say that...