same happened to me, while installing big sur on my macbook pro 2014. the solution was the one suggested in this thread, by Matthew_schuiling:
1) shutdown (by holding power button)
2) pressing option+command+r while restarting the mac
3) after a few minutes of a screen showing a globe and internet connection, a menu opens where you can find install big sur. press this one.
it should work, but have patience! due to desperation, i was almost ready to reboot again and again, perpetuating this cycle of suffering! so... try to be calm and wait for the installation process to finish, even if it seems that it will take forever.
what a relief when i saw the login screen again!! big sur is quite very nice, in speed and design.
i will also leave some useful links here, discovered later:
https://support.apple.com/en-gb/HT201475 (How to upgrade to macOS Big Sur)
https://support.apple.com/en-gb/HT204904 (How to reinstall macOS from macOS Recovery)
i'm writing this message from my macbook pro 2014 model, running big sur 11.0.1 and everything works fine, praise the apple gods.