Is it possible for a girl (who is my best friend) who only likes me as a friend to fall for me later on?

That girl sounds like me and you sound like my friend. We are best friends and everyone continuously tells us that we should go out, but we both get really awkward when that happens and we change the subject. From her perspective, you sound like a really great guy, and if she wants to be friends for now just let it be. If you like her, keep being her friend. She might be waiting to find out more about you and continue to learn about your personality. I do think it's possible for her to fall for you someday, and I think it's possible she already has. But don't push it, sorry for saying the same thing over and over, but you should keep being her close friend.