When using a third party internal NVMe SSD, then you will need to boot macOS 10.13+ in order for the internal NVMe SSD to be seen.
Is the BootROM firmware in the format similar to 99.0.0.0.0? If not, was macOS 10.13+ ever installed on this laptop at some point in the past? The keyword is "installed" since it is possible (though unusual) to have macOS boot the laptop without ever actually installing the OS on the laptop. If the system firmware (aka BootROM) is not updated to a newer version, then the system would be unable to recognize any NVMe internal SSDs. I have seen some BootROM's show the older style firmware numbering scheme even after having been updated with the macOS 10.13+ installers, so this is not 100% accurate on knowing if the firmware is new enough to work with NVMe SSDs.
From reading these forums for some years now, I have discovered the only SSD adapter that people should be using is from Sintech as it appears to be the most compatible & reliable adapter.
Keep in mind not all SSDs are compatible with all computers or adapters. What is the exact make & model of the M.2 SSD?
I'm concerned that your original Apple SSD is no longer being recognized. This suggests that something may have been damaged on the Logic Board.....possibly by the user, or possibly by the M.2 SSD or SSD adapter. I hope you disconnected the Battery & power adapter prior to removing & inserting the SSDs. Disconnecting and connecting internal components without disconnecting all power sources can possibly damage the various components.
I'm assuming the original Apple SSD was working fine before attempting to upgrade the internal SSD?
The 2012 model uses a different Apple SSD connector than the later laptop models (Late 2013 to 2015). I don't know whether it is possible to install the incorrect SSD adapter into the SSD connector on the Logic Board. If the wrong SSD adapter was used, then it is possible it could have damaged the Logic Board.