Google single sign on with Mattermost & Firebase application

I have one web application hosted in Firebase cloud and is authenticated through google account. I have feature with mattermost chat in it and I want to have the same single sign on to be used for the mattermost to authenticate. I mean the same oauthAccessToken which I receive in my previous Firebase authentication should work for mattermost as well.
Let me know how can I do this?
Appreciate any solution to this.