Suspend a project in Google Cloud

Assuming the project is based on an App Engine, to suspend it, follow the below steps:

1. Select the project in question from the Project's Drop Down List Box on the Task Bar (blue bar located at the top of the page).
2. Then, click on the Menu Icon (button with triple horizontal lines) from the Task Bar (icon is located at the top left hand corner of the Task Bar).
3. A pop up menu will then be displayed. Select App Engine -> Settings from the pop up menu.
4. An App Engine's Setting page will be displayed. Click on the Disable Application button to disable the App Engine.

Alternatively, you can try the Shut Down project but it will delete your project.

Don't forget, as a precaution, set the Billing Amount to USD$0.00.

Hope this helps.