You must have a display, mouse, and a keyboard to set up the Mini before doing anything.
You cannot just take a new Mini out of the box and and set it in target disk mode and transfer files. It just doesn't work like that.
You can however, once the Mini is set up, put the iMac in Target disk mode, connect a clone of the iMac to the Mini or connect your Time Machine backup of the iMac to the Mini and use Migration assistant.
Also, be aware that some of your apps may not be compatible with the M1 or Big Sur.
What I did when transitioning from my late 2013 27" iMac was to start fresh. I installed all my necessary apps fresh and copied all my data files that were on my iMac to my new Mac and in the process cleaned up and reorganized things and kept ancient files that I will access rarely on an external drive and rid myself of junk that I had on the computer that was just using space and no longer served a purpose. It was a bit more work but ended up with a "clean machine" to start off with. BTW, all your AppleID/iCloud stuff will automatically be loaded on the new Mac.