Using Google Play Music on Galaxy S6 WITHOUT starting subscription
I have tested the steps below with Google Play Music version 8.19.7938-1-M:


Clear Google Play Music's data. Restart the app. 
It will show some subscription plans (Individual and Family). Select "No Thanks".
The app will then ask the permission to access your media files. Click OK.
You will then be asked "Get unlimited, ad-free music". Select "No Thanks".
On the menu select "Music Library". All your music will be listed based on playlists, artists, etc and can start playing/listening to them.