You need to boot to a macOS 10.13+ installer in order to see a third party internal NVMe SSD. Plus, the laptop's system firmware must already been updated to firmware from a macOS 10.13+ installer prior to physically installing a third party NVMe SSD internally. Try booting into Internet Recovery Mode using Command + Option + R to attempt to access the online macOS 12.x Monterey installer (may not work since at one time the Monterey installer refused to update the system firmware when a non-Apple SSD was installed internally). Unfortunately sometimes even this key combination will result the Mac into booting the installer for the older version of macOS which originally shipped with the Mac from the factory (10.10 or 10.11) which is too old to work with an NVMe SSD.
You can try creating a bootable macOS 10.13+ USB installer using the instructions in this Apple article if your laptop still boots with the original SSD, or if you have access to another Qualifying Mac which is compatible with macOS 10.13, 10.15, or 11.x.
Create a bootable installer for macOS - Apple Support
Maybe the SSD adapter is incompatible or bad. From reading these forums for years, the Sintech adapter seems to be the most reliable & compatible.
Not all SSDs are compatible with all computers.