A technique for archiving NAS (network attached storage) servers includes replicating multiple locally-backed volumes, which support respective file systems of a NAS server, to respective cloud-backed volumes backed by a cloud-based data store. After replication has updated the cloud-backed volumes with contents from the locally-backed volumes, the technique further includes performing a group snapshot operation on the cloud-backed volumes. The group snapshot operation creates a point-in-time version of the cloud-backed volumes, which provides a replica of the NAS server archived in the cloud.