Hi there - not Big Sur but what I ended up needing to do on a new MBP M1 Pro, Monterrey:
- I had to install zsh version of brew
- I then used that to install llvm
- I can't remember why, but was trying different "path" configurations and ended up using this:
export PATH=/usr/local/opt/llvm/bin:$PATH
I had previously tried using the auto install script as well as the manual install and those had both failed.
Once I had brew, llvm, "path" config'd I retried auto install script and that worked.
This seems to be similar to what Oli has also posted.