MacBook Pro A1398 late 2013 does not detect the new SSD drive.

When using a third party M.2 NVMe based SSD, then you should be using a Sintech SSD adapter. From reading this forum for years, the Sintech adapter is the only one which seems to be most compatible & reliable. However, not all SSDs are compatible with all computers or adapters.

When installing Big Sur, you need to make sure to erase the whole physical SSD as GUID partition and APFS (top option) since Big Sur does not automatically convert the file system during installation. Within Disk Utility you may need to click "View" and select "Show All Devices" before the physical drive appears on the left pane of Disk Utility.

Also, the laptop needs to have previously had macOS 10.13+ installed so the necessary system firmware update was installed which can recognize a third party NVMe SSD, otherwise a third party NVMe SSD cannot be used now until the system firmware has been updated (requires an original Apple OEM SSD to be installed internally).

It sounds like you've done a lot of troubleshooting already. Here are a few additional steps you might consider to resolve the issue with your new SSD:

1. Check Compatibility: The Late 2013 MacBook Pro uses a proprietary PCIe connector for its SSDs, which is not the same as the standard NVMe M.2 SSD. Your Lexar NM620 NVMe SSD might not be compatible with the proprietary interface of your MacBook. Make sure that the new SSD is compatible with the MacBook Pro’s hardware specifications or consider getting a Mac-specific SSD.
2. Check for Adapter Compatibility: If you’re using an adapter or enclosure to connect the new SSD, make sure it’s compatible with the MacBook Pro and correctly connected. Some adapters or enclosures might not support the necessary protocols or interfaces.
3. Reset NVRAM/PRAM and SMC:

• • NVRAM/PRAM: Restart your Mac and hold down Option + Command + P + R until you hear the startup sound twice.
  • SMC: Shut down your Mac. Press and hold Shift + Control + Option on the left side of the built-in keyboard, then press the power button at the same time. Hold these keys for 10 seconds, then release all keys and press the power button to turn on your Mac.

1. Inspect the SSD Slot: Make sure there is no debris or damage in the SSD slot on your MacBook Pro. Sometimes, dust or dirt can prevent proper contact.
2. Try Another SSD: If possible, try another SSD that is known to be compatible with your MacBook Pro to determine if the issue is with the SSD or the MacBook itself.
3. Firmware Updates: Ensure that your MacBook Pro has the latest firmware updates installed. Sometimes, firmware updates can improve compatibility with new hardware.
4. Consult with a Technician: If you’re still having trouble, it might be worth consulting with an Apple-certified technician or visiting an Apple Store for professional support.

Given the proprietary nature of the SSD slot in your MacBook Pro, it’s possible that the new SSD simply isn’t compatible.

• MoThompson

Baskrag wrote:

I wanted to replace the drive in my MacBook. I bought a new one and something that was supposed to be simple and trouble-free did not happen. After installing the new drive and starting the system installation, it turned out that Disk Utility does not see the drive.

So I formatted it for Mac and for the installation that is supported by this MacBook - Big Sure (Mac OS Extended Journaled).

The Macbook still does not see the disk.

Hardware: MacBook Pro A1398 late 2013. New SSD disk Lexar NM620 M.2 2280 PCIe Gen3x4 NVMe 512GB.

Have you reach out to the vendor?

<MacBook Pro A1398 late 2013> <Lexar NM620 M.2 2280 PCIe Gen3x4 NVMe 512GB.>

You do not say where this "PCIe SSD" came from...(?)

Typically there is technical support from the retail vendor, known issues, etc.

macOS Big Sur is looking for GUID / APFS

How to download and install macOS - Apple Support

MacSales/OWC is well ahead of the curve all things Mac. They certainly have excellent customer support for their SSD replacement products/enclosures/adapters etc troubleshooting their produacts