To start a new game, you need to uninstall the My Cafe app and install it again from the app store.
After launching the game, you will see a window asking you to choose a Google account to play the game. Please ignore it by pressing the dark part of the screen, or choose the Google account that is not connected with the old account, and the game will start from the very beginning.
If you want to connect your Google account linked to the old game account, you need to open the Settings menu, press the Accounts button, and choose Google Play. When the option to restore your café appears, press "Stick with this café".
If you are an iOS user, you need to uninstall the game completely (don't offload it) and install it again. Before that, please make sure you have logged out of your Game Center account connected to the old game. Then the game will start from the beginning.
Be careful, this will reset all your game progress and in-game purchases!