I think this is somewhat of a loaded question since you don't try to win over a girl so much, you should try to build up a relationship when you two spend time together.
But you don't date girls who are in love with you first. If the world only dated people who are crushing each other, probably we'd be extinct as a human species.
There's plenty of room for you two to fall for each other *after* you start dating, and there's no reason to wait until a girl is practically telling everyone she's in love with you before you ask her out. You can ask her out the moment she seems to be enjoying your company.