Is there ANY way possible to Downgrade from my original OS (Catalina)?

I just got a brand new MacBook Air running Catalina (16 gb ram, 256 hard drive) thinking that I could backup, format and install Mojave. I have a number of older 32 bit programs that I cannot part with (newer is not necessarily better). After backing up I formatted my hard drive (APFS encrypted). After numerous tries I cannot get it to boot to my bootable installer. It keeps going to internet restore no mater what I do. I have used this bootable installer before so I don't think that is the problem. My Startup security utility settings are Medium Security and Allow booting from external media is selected. I tried the No Security setting and almost immediately get a black screen with a white "no" sign.

I have seen just a few statements on the web that it is impossible to Downgrade from your original OS. BREAK MY HEART! Is this really true?? Are there no workarounds?? I also have tried setting up an extra volume with intentions of doing a dual boot Mojave/Catalina. I restored Catalina to one volume using Time Machine backup. Catalina won't install Mojave to the extra volume and still won't boot into my Mojave bootable installer.

Is there any way I can put Mojave on this Mac??? I have time machine backups of everything if that would help. Thanx!