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.