i installed High Sierra on a 2011 mac mini in October 2025
i downloaded the installer fresh off Apple servers, created a bootable thumbdrive installer through Terminal -- i did both procedures on a 2012 MacBook Pro -- you will need to solve that issue having a machine that will download the 10.13 installer if your 2011 is non functional
i booted the 2011 off the 10.13x installer thumbdrive, opened Disk Utility, Erased the target drive, and then installed to an empty SSD
I can't remember if Software Update had any updates, be sure to check
High Sierra is mostly equal to Sierra EXCEPT High Sierra supports APFS formatting for Solid State Drives SSD -- that's probably where you want to be
if you have HDD hardware (spinning sata drive) -- you probably want macOS Sierra 10.12x (format HDD HFS+ before installing)