Catalina iOS, back up to Mac Mini Mi machine.on my LaCie external drive to populate and run on my new M1

Help me to use my Time Machine back up, that was running Catalina iOS, (located on my LaCie external drive) to populate and run on my new Mac Mini M1. Is it possible? I don't think I can upgrade my current iMac to Big Sur because it is using intel chip. So somehow I have to get my Catalina backup to install and run on my new Mi chip mac mini.