Suspend a project in Google Cloud

The only thing that you can do is shutdown the project according to the official documentation link, I don't know if this solution fits your needs

Shutting down a project in the console releases all resources used within the project. Only project owners can shut down or restore projects.

To shut down a project:

Go to the Cloud Platform Console.

1. Open the console left side menu and select IAM & Admin, then select Settings.

2. Find the name or project ID of the project you want to shut down, then click SHUT DOWN. A confirmation screen describing what will happen appears.

3. To confirm, enter your project ID and click Shut down.

Shutting down a project stops all billing and traffic serving, shuts down any Google Cloud Platform App Engine applications, and terminates all Compute Engine instances. All project data associated with Google Cloud and Google APIs services becomes inaccessible.

After a 30-day waiting period, the project and associated data are permanently deleted from the console.

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.