Something like iSCSI as you already have to 10gig card, or fibre channel SAN, apparently qnap supports both, however I've never used a qnap or iSCSI For booting https://wiki.archlinux.org/title/ISCSI/Boot For the qnap https://www.qnap.com/en/how-to/tutorial/article/how-to-create-and-use-the-iscsi-target-service-on-a-qnap-nas
The general idea is a small boot partition to load kernel and most importantly the drivers for the nic, then mount the Nas over iSCSI and finish loading the os
To be honest a 1TB SATA ssd isnt that much, you could have 10 distros @ 100gb each with extra storage mounted on the nas. 100gb is loads for a Linux OS. I think most of the virtual machines I spin up without a GUI use a 20GB disk
You can also boot directly over the network with pxe/netbootin etc but I'm not sure how that works with an add in network card, as it's usually a feature of the bios itself