I recently found out that a girl I'm going out with for the first time is having her birthday later this week. I saw on her FB she's having a party. I'm not currently invited nor have we even talked about her bday.

Now we still don't know each other that well yet but things have progressed nicely so far and she's definitely interested in me. My current plan is not to mention her bday during our date unless she brings it up. If she doesn't I'll wish her a happy bday via the phone/FB or whatever on the actual day of her bday.

Would this be the best approach? How should I handle a second date in that case? What if she does bring it up? Never had to deal with a situation like this before. I imagine even a girl who is super into you would be wary of introducing you to her friends and family after only one date which would obviously happen at a bday party.