Yes, you can connect on-premises storage to cloud servers, but how it depends on the type.

A NAS (Network Attached Storage) can share its files with cloud servers over a secure VPN or a dedicated network connection. As cloud providers offer their own managed file services that work like a NAS.

A traditional SAN (Storage Area Network) cannot plug directly into cloud servers. Instead, we have to use the cloud’s own block storage services, which serve the same purpose. I prefer we should always consider network latency and data transfer costs.