It's not possible to suspend a project as you mentioned but I can suggest you these options to save costs:
1.-Stop the instances, so you only will be charged for any resource attached to it.
"A stopped instance does not incur charges, but all of the resources that are attached to the instance will still be charged. For example, you are charged for persistent disks and external IP addresses according to the price sheet, even if an instance is stopped."
Stopping and starting an instance
2.-Depending of what type of data it's on the persistent disks, for example, if it's unstructured data, I can recommend you to use a Google Cloud Storage bucket with a Nearline class (only $0.010 per GB per month), the class of your bucket will depend on your needs and how frequently you will access to the data. Cloud Storage documentation
3.-Take regional snapshots and delete everything you don't need, whenever you need a new instance create it from one of the snapshots you created. There isn't a major pricing difference between snapshots ($0.026 per GB per month) and persistent disks ($0.040 per GB per month), if you are using a SSD persistent disk the price is higher and you will save more money.
You can find more information about creating instances from snapshots here