Howto use Google APIs from PHP: http://stackoverflow.com/questions/22168819/android-test-push-notification-online-google-cloud-messaging
Of course, you first have to activate this Google service: https://console.developers.google.com/projectselector/apis/
Test with Bernd Bindreiter’s open source Android App first: https://play.google.com/store/apps/details?id=com.firstrowria.pushnotificationtester It should always work, even without activation of Google APIs. Source: https://github.com/bbindreiter/PushNotificationTester_App
Since Google is selling more than 1.6 billion Android phones a year, you can reach around 2 billion+ people with Android notification, if they once clicked the “server push” button on Nextcloud web server. No registration in Nextcloud mailing list neccessary any longer.
Finally to implement this is less than a piece of cake, but Nextcloud SQL database structure needs to be extended to keep Android user token and id.