I have the Big Sur installation file. When I tried to run it, my Mac told me it couldn't install it. I was hoping to find an earlier version of Monterey, but failed to find one.
So I gave up getting an earlier version now. But to be ready for future problems, I've been trying to install the current version of Monterey on that disk. I have run the install program, and so far it's run for a while, then rebooted to my main drive only partially installed on my removable SSD. (If I try to install it again, it tells me that). So I have to erase it and try again. I'm on my third attempt now.
Now that you have the Big Sur installer file, how about creating your own Big Sure bootable installer drive? For this I recommend using a USB thumb drive, 32 gigs minimum. (My Monterey installer drive uses up 14+ gigs and a 16-gig thumb drive will probably fail.)
Using Disk Utility format that thumb drive as Mac OS Extended (Journalled), HFS+J -
not APFS. Bootable installers adopt the older file system so it will probably fail from APFS.
I named my drive
Install macOS Monterey. For your purpose you can name it
Install macOS Big Sur. (You can give it another name but I find that it helps to identify which macOS version I have on it.) Once the USB drive is ready, go to the location of the Big Sur installer file. Make sure you have the Finder path bar (bottom of window) showing. (If not, go to the Finder ->View menu to activate it.)
Here is the terminal command to create the installer:
sudo [installer file pathname]/Contents/Resources/createinstallmedia --volume /Volumes/[USB drive name]
where you replace the terms in brackets with the correct information. Watch for word spaces. If the command fails, there could be spaces where they should or should not be. (After
sudo and before and after
--volume. The others would be from the information you added. If you are not familiar with text editing in Terminal, you can use a text editor to compose the information.
In the Finder window where you have the installer file, right-click on that file on the path bar and choose
Copy “[file name]” as Pathname and it will be copied to the clipboard. Replace the
first bracketed argument above with the copied pathname. Then replace the
second bracketed argument with the volume name of the USB drive.
In Terminal, after you have the proper code entered, press return, enter your password and press return and let it do its thing. If the process was successful, you can reboot from that drive by selecting it as Startup Disk in System Prefernces, or just reboot with the Option key down to get a list of startup drives. Good luck, and enjoy.