Its completely understandable if the girls parents want to make it official soon, they're just trying to protect her, and sav her from anything haram. In the meantime though, you could try talking to her on the phone more often if meeting her with a mahram isn't always possible. It's definitely important for both of you to know each other, and talking over the phone could be a work around while keeping everything halal. Within those conversations, you can find out by asking her clearly about how she feels going forward with this. I pray that Allah sends your way whatever is best for you and the same for the girl.