When you sign into Google Play Games, your Iron Marines progress will be saved automatically. This means that you'll be able to pick up where you left off, even if you uninstall the game or switch phones, as long as you use the same account and have a connection to the cloud.
Before you start
Make sure you have the Google Play Games app installed and updated.
Here are a few troubleshooting steps for you to try
Open your game, go to the Settings menu, and check that Google Play save is enabled.
Once Cloud save is on, close the game.
Open Google Play Games and tap Profile