How to Downgrade a New Mac to Mojave from Catalina

Not sure what you mean by this. If the download finished did it launch the installer splash screen and then tell you it couldn’t install it? If so, then all you need to do is quit the installer and it will be found in your /Applications directory (folder).

The next step would be to copy it to a bootable drive of some sort. I always create a bootable USB thumb drive for that purpose. The Terminal Command for that is
sudo /Applications/Install\ macOS\ Mojave.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume
where the thumb drive is temporarily named “MyVolume”

Since your iMac initially came with Mojave 10.14.4, you are supposed to be able to use Internet Recovery, as described in How to reinstall macOS from macOS Recovery following the Shift-Option-⌘-R instructions, but some recent users have been reporting that not working for some reason.

In all these cases, you will need to first erase the entire SSD, so make sure you have your user data backed-up in a place you can migrate it from after you get Mojave running.

There’s one more way to create a mountable image of the Mojave Installer for you using a Python script that Mac Admins in IT departments frequently use, but it’s a bit more complicated, so get back to me only if these other methods all fail.

If all else fails, you can still run those major 32-bit apps in a VM like Parallels installed along side Catalina.