Hi there,
If you want the app to trigger a notification on the same device, then you should be looking at the local notification plugin here: https://github.com/katzer/cordova-plugin-local-notifications
If you want the app to trigger a push notification on somebody else’s device then check out my response to this post: Push notifications problem as of february 2016 new problem because of updating
If you look at my code in that post reply you will see that I send the Google Cloud Messaging ID along with device information … etc to my RESTful API … which is Firebase in your case. ( I use custom API written with NodeJS and ExpressJS). The RESTful API takes care of delivering the appropriate message to the appropriate user(s)