Cost for just creating efs and leaving it empty

Interesting question. I spun up an empty burstable EFS volume and see the minimum size used is 6KiB. Therefore, I would pay for this 6KiB, which when measured in monthly GB is negligible. So I would think, but haven't confirmed yet, that until you actually put data into the EFS, it'll be free. This is similar to creating an S3 bucket with no objects. You only pay for what you use.

If you're just creating but not storing any files or transferring any data to/from, and you are not provisioning throughput, it should be no cost as the pricing is consumption based:

Amazon Elastic File System (Amazon EFS) is a simple, serverless, set-and-forget, elastic file system. There is no minimum fee or setup charge. You pay only for the storage you use, for read and write access to data stored in Infrequent Access storage classes, and for any provisioned throughput.

Regarding Provisioned Throughput, if you enable this you'll pay for that provisioned capacity regardless of use ($6/mo per 1MB/s provisioned throughput) as you're asking for capacity to be reserved for better performance.

If you use the calculator you can input numbers to see expected costs. I.e. entering 0G and 0 provisioned throughput is a $0 bill. 0G but 1MB/s provisioned throughout is $6/mo.