I wonder if I can use Azure Blob Storage to store Mac Time Machine files. Is it really possible to mount a blob storage as a drive for Mac Time Machine?
Of course it's possible (possible as in it's doable, not possible as in "download, install and you are done). It's possible to write Mac OS X driver (for example using fuse) that mounts Blob Storage as local drive and then emulates HFS to Mac OS X. However, in practice that's really hard task.
So in short: no, it's not.
You may have better luck with installing netatalk (and AFP) with Time Capsule emulation, and then mount Blob Storage to Linux server. That way Mac OS X just thinks there is some storage, not actual HFS volume (and it'll create
sparsebundle to emulate HFS).
Azure blob storage is less than ideal for this purpose; as others have implied you would need to store all of the file system metadata on your own.
These days, though, the "Azure Files" service does seem to be a workable option using an Azure "General purpose" storage account.
It's generally unsupported, but you should be able to use TimeMachine to back up to a SparseBundle disk image (formatted as HFS+) in the same was as with most other file shares using the SMB protocol.
- Apple Time Machine Backup to Microsoft Azure (video; YouTube)
- Mount Azure file share over SMB with macOS (Microsoft)
- Creating a local drive mapped with an Azure File Share for your files in the cloud (not Mac-specific, but may have some useful information)
- Use an Azure file share with Windows (Microsoft)
If you would like to backup to a SMB file share with macOS 10.3.3 or earlier (either locally or in the 'cloud') you'll want to read this:
Finally, if your system is so old that it doesn't support SMB version 3 (MacOS X 10.9 Mavericks or earlier), Azure Files allows the use of SMB 2.1, but only by setting up a separate VPN.
- Azure Files networking considerations (Microsoft)