14 inch MacBook Pro M1 pro with Mac OS Big Sur

No, any new Mac will ship with the current version of MacOS. So if you order a new Mac today, it will come with a version of MacOS 12 Monterey.

Also, it is not possible to run a version of MacOS older than the one it first shipped with, so you would not be able to run Big Sur on a 14" since Monterey debuted at the same time as the 14" M1 Pro MBP.

Most likely not as only macOS Monterey is what these models come with and Apple does not support downgrading from the originally-equipped versions.

Those models shipped with:

macOS 12.0.1 (21A558)

source:

https://everymac.com/systems/apple/macbook_pro/specs/macbook-pro-m1-pro-8-core-cpu-14-core-gpu-14-2021-specs.html

.