Download Mojave on a non-Mojave suitable computer
Tetsujin is correct in that using your recovery partition to do a clean install on your Mojave-supported Mac Mini is ideal.  You can then download Mojave from the App Store as usual.

If that is not a viable solution for you:

After reading through the extent of the information given to you in your previous question, would recommend you use dosdude1's Mojave Beta installer tool.  Create your USB installer, install on the Mac Mini's new SSD, and then immediately upgrade to the full version of Mojave

Alternatively, if you're feeling brave, you can follow the instructions here to obtain a copy of the Mojave or High Sierra installers via the download links.

It will take a little bit of work, but you can get it done!