I tried to get Big Sur on my Retina, 15", Mid-2015 MBP but it can't be found in the System Update.

I would suggest you upgrade first to 10.15 Catalina, then apply any Catalina updates that are available through Software Update.

Once that has been completed, make the transit to Big Sur.

❗️ Do NOT upgrade until you have made a Time Machine or other backup of your startup drive.

Learn How to Back up your Mac with Time Machine

How to Upgrade  macOS:

The macOS version you can upgrade to depends on the year your Mac was released.

Click the  (Apple) menu at the top of your screen and choose About This Mac.

Check the Compatibility of your Mac with newer versions of macOS:

➡️ macOS 10.15 Catalina is compatible with the Macs listed here

➡️ macOS 11 Big Sur is compatible with the Macs listed here 

❗️ – IMPORTANT – None of your 32-bit apps will work in Catalina, Big Sur or Monterey.

32-bit app compatibility with macOS High Sierra 10.13.4 and later - Apple Support

Use the free utility Go64 to check the compatibility of your apps:

https://www.stclairsoft.com/Go64/

✅ - IF your Mac and apps are compatible, then using Safari only, download the macOS upgrade installer app:

Click > Catalina, or Big Sur.

Once downloaded, double-click the “Install macOS…” app in the Applications folder to begin the upgrade.

Please see > How to get old versions of macOS.

You're welcome.

It's true that an OS upgrade can usually be applied even to an OS that's several generations older, and the process usually goes well. But sometimes not. Whatcha gonna do, right?

I hope this has put you on the right track. Please post again if you still run into troubles.