Can't find my SSD on disk utility ? I Have Error vdh002

You must properly erase the new SSD and install macOS on the new SSD. See this Apple article for booting the laptop into Internet Recovery Mode to access the online macOS installer. You will also need to follow the "Erase Disk" link within that article as well.

How to reinstall macOS - Apple Support

Keep in mind that if this Timetec SSD is an M.2 SSD which requires an SSD adapter, then you should use the Sintech adapter which seems to be the best/most compatible adapter. I'm not familiar with Timetec, but keep in mind not all SSDs are compatible with all Macs.

Also, an NVMe SSD requires macOS 10.13+ which must have already been installed on this laptop at some point in the past in order for the laptop's system firmware to have been updated to support an NVMe SSD.

What OS installer are you accessing when booted into Recovery Mode? It looks like a very old OS since it does not mention "internal" and "external" on your list of drives which means the OS installer being booted is too old to recognize the NVMe SSD you installed. See my previous post for details.

Try booting into Internet Recovery Mode using Command + Option + R to attempt to access the most recent compatible online macOS installer for your laptop. Unfortunately, even this key command will sometimes still just boot the older online macOS installer for the OS which originally shipped with your Mac from the factory which apparently is too old to work with an NVMe SSD.

Your other option is to create a bootable macOS USB 10.13+ USB installer using the instructions in this Apple article if you have access to another Qualifying Mac:

How to create a bootable installer for macOS - Apple Support

A Qualifying Mac is one where the OS installer you are downloading is compatible with the Mac downloading the installer. For example to download & create a bootable macOS 10.13 USB installer requires a Mac from Late-2009 to 2018. See this article for which versions of macOS are compatible with various Apple hardware to determine a Qualifying Mac.

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

Of course this all assumes that the laptop with the new NVMe SSD at one point had macOS 10.13+ installed on it so that the laptop's system firmware is able to work with an NVMe SSD. If this is not the case, then you will need to first install a working original Apple OEM SSD so that you can install macOS 10.13+ on it, then you can reinstall the NVMe SSD and install macOS 10.13+.

Ok, that screenshot of Disk Utility indicates that you are likely booting to macOS 10.13+ installer (unless of course Apple updated Disk Utility with macOS 10.12.6 to look like the 10.13+ versions). The only way for you to confirm the OS installer you are booting is to see what OS it will install which should be shown on the recovery menu under "Reinstall macOS xxxx", where the xxxx will be the version of macOS installer.

If you are indeed booting a macOS 10.13+ installer, then it means one of the following:

• macOS 10.13+ was never installed on this laptop before so the system firmware update has never been updated to work with NVMe SSDs utilized by third party SSDs. You will not be able to use an NVMe third party SSD until the system firmware has been updated which requires using an original Apple OEM SSD internally.
• The SSD is bad or incompatible
• The SSD Adapter for the M.2 SSD is bad or incompatible (best to use one from Sintech for best results)
• Logic Board may be bad

There is nothing else we can do to help you with this. If you don't understand what I have tried to convey (I know it can be confusing), then you will need to find a local Apple tech to assist you and possibly show them the information I have posted in this thread. FYI, an Apple Store will not help you with a third party SSD, but if the laptop is still supported an Apple Store may repair the laptop using original Apple OEM parts instead. An AASP may or may not help with a third party SSD, but it never hurts to ask them.

Good luck.