Crucial P3 SSD not detected in Macbook Pro early 2015

Was macOS 10.13+ installed before the original Apple SSD failed? If not, then you will need to install an Apple SSD followed by installing macOS 10.13+ in order to update the system firmware to allow for using a third party NVMe SSD.

If macOS 10.13+ was previously installed, then in order to see the third party NVMe SSD, you must now install macOS 10.13+ since only they will include the necessary NVMe driver to communicate with the third party SSD. Try booting into Internet Recovery Mode using Command + Option + R to access the online macOS 12.x Monterey installer which will be able to see the third party NVMe SSD (you can try Command + R to try to reinstall the OS you were last had installed too). However, sometimes no matter what special keys you use, it may only boot to the online installer for the OS which originally shipped with the laptop from the factory, but this will be too old to work with a third party NVMe SSD.

If you have access to another compatible Qualifying Mac, then you can create a bootable macOS 10.13+ USB installer using the instructions in this Apple article:

Create a bootable installer for macOS - Apple Support

A Qualifying Mac for a 10.13 to 12.x installer is generally one from Late 2009 to 2021, but you can use the information in this article to confirm which other Macs are compatible with one of these valid operating systems:

https://eshop.macsales.com/guides/Mac_OS_X_Compatibility

Generally speaking (there are some exceptions so use the article above):

macOS 10.13 -- Late 2009 to 2018

macOS 10.15 -- 2012 to 2019

macOS 11.x -- Late 2013 to 2020

macOS 12.x -- 2015 to 2021 (at one time the Monterey installer would not work with a third party internal SSD to install Monterey for the first time unless Monterey had already been installed before while an original Apple SSD was installed internally...perhaps this was fixed with a later version of the Monterey installer...may be best to try macOS 11.x if Monterey fails to install due to the third party internal SSD.)

FYI, from reading these forums for years now, it seems the most reliable & compatible SSD adapter is from Sintech.

10.12 Sierra wants HFS+ format

10.13 High Sierra wants APFS format

Only drives that candidates for installation in their current format will be shown, but High Sierra (and possibly others) can do a conversion as it installs.

macOS 10.12 Sierra is not able to recognize a third party NVMe SSD as it does not have the necessary NVMe driver. If Command + R or Command + Option + R does not allow you to boot macOS 10.15 or 12.x, then yes, you will need to create a bootable macOS 10.13+ USB installer using another Qualifying Mac.

Edit: Another option is to use the Crucial P3 SSD externally so you can install macOS 10.12 Sierra on it, then you can install macOS 10.13 to 10.15 to the P3 SSD while using it externally. Then you can reinstall the P3 SSD internally and attempt to update to macOS 11.x or 12.x.