Apple offers solutions for Big Sur problems on MacBook Pro 2013 and 2014

With the departure of Big Sur last week, owners of a 2013 or 2014 MacBook Pro found that the computer would freeze completely during installation, rendering it unusable.

Apple acknowledged the problem in a new support document that provides basic instructions on what to do if macOS Big Sur‌ can't be installed on a 2013 or 2014 MacBook Pro.

Apple suggests owners to disable external devices, try rebooting, offend SMC again, and again NVRAM or PRAM.

This says the supporting document:

Press and hold your Mac's power button for at least 10 seconds, then release it. If your Mac is on, it will shut down. Unplug
external devices connected to your Mac, including USB monitors and accessories, and disconnect any cards connected to the SDXC slot. Then turn on the Mac.
If the problem persists, restart the SMC following the procedure for computers with non-removable batteries.
If the problem persists, reset the NVRAM or PRAM.
Apple says that if none of this works, customers should contact Apple Support for further assistance with the issue. Apple will update this article as more information becomes available.