Big Sur on an external SSD

You can use your current macOS installation to do it.

First go to the Mac App Store and download Big Sur installation here https://itunes.apple.com/br/app/macos-big-sur/id1526878132?ls=1&mt=12 . This will prompt you the update interface and ask you to download the Big Sur installer. Click download and it will create a "Install macOS Big Sur.app" in the Applications folder and automatically launch the installer when download is finished. Close it for now.

Plug the SSD to the Mac, Open Disk Utility, Locate the external disk and format it APFS How to erase your Intel-based Mac - Apple Support (NOTE: forget the instruction to enter Recovery Mode, you don't need it now, only open Disk Utility and use it as indicated in this article to format the external drive). Here's some more detailed information on Disk Utility Erase and reformat a storage device in Disk Utility on Mac - Apple Support

Once the external disk is formatted, go to Applications folder, launch the macOS installer you downloaded and follow the instruction.

Attention to choose the correct drive right in the beginning, pointing the installation to the external drive.

Once installed, you'll have to restart holding Option and select the external disk.

With this method you'll always have to pay attention to the USB connection because it can easily disconnect if you move your Mac, the SSD or even if the desk is shaken or vibrates somehow, you know. You'll have to guarantee they're always well connected.

What is the exact year model of your Mac?

If I may, have seen numerous issues attempting to do the same thing in Catalina and people have had unsolved issue after the Catalina Security Update 2020-01. Was working with this and they never had a foolproof solution. Yesterday, was working with another person attempting the Big Sur on iMac 2014 on External Drive. Same issue in Catalina appeared in Big Sur. Sure, they could install Big Sur to external drive but no matter what they did, even going into Startup Disk as Admin Account and changing to external drive - No way would Big Sur boot to External Drive @ Startup.

This does not mean it will not work for you but . . . ?

Nice to hear you managed it.

Pay attention to the USB connector so it won't keep disconnecting because of vibration, bumps in the desk, etc., OK?

Yeah, that thing with the installer files, I don't know why Apple does make it so hard to simply download the installer. I really don't.

I had an SSD with mojave installed on it, and an imac with Mojave as well. And i tried booting from the SSD and updating to big sur, but during the first restart (during the install) the computer just didn't start up. And i tried booting an SSD with big sur installed and the same thing happened. Can anyone help me with this problem?

When i booted into macOS recovery and opened startup security utility all i saw was the first option: "Firmware password security is off", "turn on firmware password".

And i was never prompted to select a user or prompted for my password.

Well said, P. Phillips.

Maybe this can be the solution About Startup Security Utility - Apple Support

It is needed to enable external boot.

iMac (Retina 5K, 27-inch, 2019), i asked this as a question here: https://discussions.apple.com/thread/252455394

Oh, look, there's this you have to setup properly in order to be able to boot modern OS from external drives About Startup Security Utility - Apple Support

Yes, good article referenced @ Rafael Scheid. But only affects those with Fingerprint T2 Chips.

Oh yeah, I forgot that, sorry. I have a 2019 16", changed secure boot option and was able to boot from external drives when testing beta.

Well, seem like the problem is deeper than I know.

Further to the Catalina external Boot Drive issue. Over here at Macrumors on this very topic