Is this mostly for fileserving or apps? If you’re using it as a Fileserver share the relevant parts of the ssd while you rsync all of it over to help ease downtime.
You can also install the nvme through a virtual machine and pass /dev/nvme_whatever to the vm. Then rsync everything over using ssh then reboot the whole machine using the nvme drive for the os (make sure to use UEFI for the vm on kvm).
For apps kinda the same vm deal leave the ssd up and configure the nvme install as needed then copy whatever data you need over before rebooting.
It’s more convoluted to do it that way but it will reduce downtime