Recently, I've grown quite close to a girl I know through a friend. Unfortunately, I discovered that she has a boyfriend. She mentioned that their relationship is unstable, and she doesn't see him as marriage material. Upon learning about her relationship status, I initially attempted to distance myself. However, she unexpectedly came closer, and make it quite clear that she's interested in me but hesitant because she feels she doesn't know me well enough yet.

should I go for it or give up?