The moment you start referring to her to anybody as your girl-friend in any conversation with other people around, basically, will be when you make it official (she will also likely not object at that statement either). She is probably just waiting for you to say something like that in order to make it become « official » between you two.
Actually, try hugging her before you two go home, and in fact, keep holding her in your arms after hugging her & looking directly at her to see if she gives any kind of resistance to it or not, and if she's pressing her hips into you as she hugs back, you basically have yourself a girl-friend if it seems like she's still willing to let you proceed with more than just hugging.
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