You can, and there are a number of options.
Easiest IMO is to install both drives, and then use dd
to copy drive A to drive B, and then resize the partitions with gparted
to fill the rest of the disk.
Do this from a live USB so that your not currently using drive A.
https://serverfault.com/a/4912
Note that /dev/sda
might not be your first disk, so make sure you get them correct. Gparted can help you identify your disks.
VSS equivalent would be btrfs snapshots or zfs snapshots.
Can you really copy a VSS to a new disk? For a new install, at some point you’ll need to reboot and go offline, so I don’t see the point in trying to keep uptime. If uptime matters, dont upgrade a disk, replace the entire system.