Can't find partial download of Big Sur

As @Luis Sequeira1 has mentioned the Empty Space Requirements are not optional. Without the required space it is not going to install.

• See used and available storage space on your Mac Specifically Other: Contains files that don’t fall into the categories listed here. This category primarily includes files and data used by the system, such as log files, caches, VM files, and other runtime system resources. Also included are temporary files, fonts, app support files, and plug-ins. You can't manage the contents of this category. The contents are managed by macOS, and the category varies in size depending on the current state of your Mac.

What is “Other” storage on a Mac, and how can I clean it out?

How to free up storage space on your Mac

How to create a bootable installer for macOS and Must be done on a Qualifying computer for Big Sur.

Special Notation if running with Touch ID chip - About Startup Security Utility and enable booting from External Drive. This would HAVE to be Done BEFORE erasing and attempting a clean install of any OS to this machine.

I would have expected it to be in Applications but be warned: 21GB is not nearly enough free space. The installer has to be decompressed and then while installing it has to keep old anew system files present until the new OS is done installing. You need some 35GB+ space before downloading the installer.

Check in Applications Folder for a partial Application called Install Big Sur an for check the Trash and empty it.

Ah - the darn 128 GB SSD Apple Used to sell - that is a tough one. Purchase an External SSD Drive ( for speed of usage ) at least 1 1/2 Times bigger than internal drive or if pockets are deep enough get the TB Sized SSD. Move as much go your personal files off the internet to external ie: Pictures, Music, Videos, Poadcaste, iOS Backups etc - basically files which are under your direct control. Then inventory the installed Apps and choose what to keep and what to Remove. It is doable but at a cost.

Are you sure it is not in the Applications folder?

The installer is called "Install macOS Big Sur".