My exsisting Google Cloud Prject does not show up in Firebase

I have an existing Google Cloud Project as can be seen:Google Cloud Project List by the name IIMA Student App. I want to integrate the same app over at Firebase, however I have run out of number of free Firebase App so I was hoping to add the IIMA Student App as an existing App but it does not show up in the list. The picture at Firebase is as Firebase Console Project List. My primary goal is to use Google Auth2.0 for creating a Login in my Android App so as to only allow custom domain(eg: user@mydomain.com) to only log in to my app.