If my phone is already running when I power on my Edge 1030, the 1030 will not connect to the phone. Even if I manually start the GCM app, the two won't connect. If I restart the phone, the 1030 connects as soon as the phone displays the momentary "Garmin Connect" popup at the bottom of the screen, without the GCM app needing to be started. Phone is a Google Pixel 2 running Android 10, GCM is 4.23.1. The Edge is running the beta 8.06 FW, but the problem was exactly the same with the previous 8.00 release FW.
Once the connection has been made, everything appears to run correctly - Livetrack autostarts when I start an activity, the Livetrack session can be tracked OK while the activity is in progress, and when the activity is ended, it uploads to Garmin Connect via the phone without any problem.