Installing old OS X version and the "It may have been corrupted or tampered" message that can't be fixed by changing the date
This is not so much a definitive answer as some speculation based on prior known behaviour.
One thing to note is that the 'date/certificate issue' should now be fixed for all older installers &amp; so shouldn't need any workaround in that respect.
I haven't tried any of these older installers in a while, but in the past some were only valid if your computer could not run any newer OS. The El Capitan installer was specifically 'sold' that way.
The Apple site you linked  also obliquely points in the same direction. Each of those links says &quot;can upgrade…&quot;  (I don't have any recent hard evidence to know if this is true or not).
See How can I download an older version of OS X/macOS? for some history behind this, though the answer is probably falling behind the times now. I can't maintain it any more as I have no Mac capable of running anything newer than Mojave.
On a Mac Pro I'd test this by removing the drive with Catalina on it &amp; installing from USB to a fresh clean drive. Not sure that's so easy on a laptop.
One thing I would definitely try… You appear to be creating the installer on the same partition you want to install to (if I'm reading you correctly). I'm pretty sure this isn't going to work. Create the installer on a separate USB stick &amp; boot to that, then attempt install to the internal partition.
Alternatively, you could try installing from Internet Recovery. If you boot holding  Cmd ⌘   Opt ⌥   Shift ⇧   R  the installer presented should be the one that originally shipped with your Mac. If that's successful, then the earlier potential caveat of 'can update from' would then be on your side.
One other thing to note is that as these installers are all designed &quot;to update&quot; then I'd be pretty sure they will run as an app if mounted to a Mac already running any OS older than the installer. It wouldn't need to be made into a USB boot drive. That would make your upgrade from your original OS over Internet Recovery much simpler… maybe ;)
From comments
Apparently the new installer dmg files install the &quot;Install macOS (name)&quot; into your apps folder, from where you can run the update.