I had the same issue where BIOS detects my SSD under the SATA section but it does not register as a bootable device.
Here's the solution that I stumbled upon:
Boot into the BIOS and go to the "BIOS" section. Enable "CSM Support". This opened up some more configuration options, but I left them as is in UEFI mode. Save the configuration and exit. Hopefully it should boot into your OS now.