How can you use Amazon S3 or S3-compatible Storage as NFS? Is there a way to achieve this?
Something that can be accessed through an external network (internet, public) using NFS protocol.
If you want to use S3 as mounted storage for personal computers, you have two possibilities.
One is to use an EC2 server as NFS server, backed by S3. AWS provides a server called AWS Storage Gateway for doing this, but you will of course have to pay for running that server 24/7. I think it might be oriented towards providing NFS inside your VPC, though. Providing an NFS service over the Internet is an uncomfortable proposition from a security perspective.
Much better is to have code on your computer to present S3 as local storage. There is a commercial plugin called ObjectiveFS and a free opensource one called S3FS-FUSE; I think S3FS-FUSE is the answer you are looking for, if it is not then their page at the bottom has a list of "competitors".
There are several caveats to using S3 as mounted storage, though:
EFS (Elastic File System) is NFS on AWS. But it has nothing to do with S3.
If you need to serve files on that type of FS I think you need to run your own webserver pointing to the mounted share.
You can use S3FS.