By default, every VM instance in a VPC network has a single default network interface, and you cannot add or remove network interfaces from an existing VM instance.
This means that GCP does not allow you to attach the network interface of a VM instance to a different network when you restore the VM instance to a location where the source network does not exist. For more information, see Google Cloud documentation.
Use the Google Cloud Console to create a new VM instance from the restored instance. As part of the instance creation, you can choose the necessary network. Then you can attach the disks of the restored VM to the newly created instance.
To learn how to create a new VM instance from an existing instance, see Google Cloud documentation.