Internal SSD not showing up in Disk Utility after erase

Since you have a third party SSD installed you need to boot to macOS 10.13+ in order to see the third party NVMe SSD. Your screenshots are showing you are booting an earlier version of macOS which means it does not have the necessary NVMe driver to even see the third party SSD.

Try booting into Internet Recovery Mode using Command + Option + R to access the macOS Big Sur online installer (in theory since sometimes this too will only boot to the oldest OS which originally shipped with the Mac).

If this fails, then you will need access to another Mac able to run macOS 10.13 - 11.x so that you can create a bootable macOS 10.13+ USB installer using the instructions in this Apple article:

How to create a bootable installer for macOS - Apple Support

The screenshot of Disk Utility does not appear to be from High Sierra as it should have a "View" option button just above the left pane of Disk Utility (I do see the High Sierra background). I haven't used Disk Utility from the High Sierra installer in a while, but I believe it should have that "View" option.

If this is a valid High Sierra installer, then it would mean your internal SSD has failed, or the SSD adapter is bad or incompatible. It seems the Sintech SSD adapter is the most reliable and compatible SSD Adapter to use with an internal third party SSD stick.

iGilberto Said:

"Internal SSD not showing up in Disk Utility after erase: Clicked it. Nothing happens"

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thank yo for the followup.

Use a Mojave USB Bootable Installer:

Then all there is the "Base System". So, install the macOS anew, using a USB Bootable Installer for Mojave Use another Mac (friend's or family member's) to create one. See here: How to create a Bootable Installer for macOS - Apple Support. Mojave is witch to use. See here: Mac Pro (Late 2013) - Technical Specifications - Apple Support

iGilberto Said:

"Internal SSD not showing up in Disk Utility after erase: Would this make Macintosh - HD reappear again as the main internal SSD?"

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Yes. Because all would be able to be reinstalled. So, try it. There are two parts to it the hard drive, when it comes to the install. A bootable installer is the best method for Mojave.

Tried Internet Recovery Mode?: How to Re-Install OS X with Internet Recovery on a Mac - OSXDaily

BEFORE you erased the drive, what version of MacOS were you running?

iGilberto Said:

"Internal SSD not showing up in Disk Utility after erase: I have a 2013 Mac Pro and have used it for quite some time. I decided to factory reset the Mac Pro by going to Disk Utility. I clicked on the internal SSD (Macintosh - HD) and erased it.[...]I then went to disk utility to install the OS again only to find out that that Macintosh - HD is no longer there. There is no internal drive anymore. [...]""

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Mount the Volume:

Select the "OS X Base S..." volume, and then click the Mount button. Then, try deleting this volume.

iGilberto Said:

"Internal SSD not showing up in Disk Utility after erase: [...]Luckily, I was able to resolve this problem. Thanks!"

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What is the Solution?

Do your Part: --Spread the word of how this was solved. Doing so will help many for certain.

iGilberto Said:

"Internal SSD not showing up in Disk Utility after erase: Hi, it looks to already be mounted. It shows "Unmount" greyed out."

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Mounting This:

So try the following.

Click This: