I see. As far as I know, some motherboards from around that time or older don’t have support for NVMe booting, etc. in their firmware (BIOS or UEFI). I suppose ones for 4th generation Intel Core have UEFI (with compatibility mode), but if it is a true BIOS, then I think it will not support it at all. A UEFI may or may not support it, and it may depend on settings. The fact that you use an adapter may change things too.
By the way, some motherboard UEFI remove EFI boot entries whenever you try to boot with the disk not detected for whatever reason, and then they don’t add it back (or at least not the Qubes OS one) when the disk is detected again.
You should check rEFInd as a workaround for poor motherboard firmware boot managers, but beware that booting rEFInd before Qubes OS is essentially like dual-booting, which carries a risk of full compromise of Qubes OS, so it’s generally not recommended. But I think it is very good at enabling you to boot a lot of things that your motherboard would otherwise not let you boot. The idea is that you boot rEFInd from anything supported (SATA disk/USB/optical drive) and it shows you a nice boot menu that includes anything that rEFInd could detect.