If you've already synchronized your game with a Google Play account then you can manually save/load your progress.
In order to do this, you should go to the settings, at the right bottom corner you will see a green button "Game progress". Press it - a new window will appear and here you can choose whether to save your progress or to load it. If you press "Save", your progress will be saved in a Google Play cloud. If you choose "Load" then the window with your last save will appear( you can see here the version of the game and your level). When you press "Choose" - the progress will be loaded.
Saving game to the cloud is only possible in Google Play.