This is some nice advice but

Treat them like you would any of your male friends.

Don’t do this. Understand that you wouldn’t do this with any random guy either. As with any new acquaintances everyone is cautious in the beginning and women more so. Whether you find the new girl appealing or not all you have to do is cautiously get to know her through your interactions with her, like any other relations you may build with initial strangers and get used to their presence and predilections.