Can I upgrade directly from OS X El Capitan to Big Sur?

Yes, one can go El Capitan directly to Big Sur on Qualifying computers.

Though, seriously suggest going El Capitan to High Sierra as a mid-step. This will better position the computer and software for the eventual jump to Big Sur.

Reason for mid-step - normally the filing system used in High Sierra is converted to the newer APFS filing System versus the older HFS Journaled filing System. This is important as Big Sur requires the internal drive be formatted as APFS.

Also, and application present on El Capitan are generally support on High Sierra.

Catalina and above do not support anything 32 bit - period and no workaround.

The Age of this computer will Govern what newer version of macOS it will Qualify to install. Use About this Mac from the Apple Icon on Desktop - the required Information will be there.

With the above information in-hand - follow this How to get old versions of macOS and verify what version this computer Qualifies to install. Make sure to use Only Safari to commence the download as Others may not work. Safari will open a redirect and open the Apple Store where you can commence the download. If an error message appears, that is probably because one is using another Browser.

Suggest using Go64 to find 32 bit application before attempting the upGrade. Some or many of the Application already installed may required update or upGrades to 64 Bit Versions.

Make a Time Machine Backup Before attempting. Notation - Mojave is the Last version to support 32 bit applications / extensions and Drivers. Catalina & Big Sur support 64 bit and there is no workaround.

Are there any AntiVirus, Disk Cleaner, Optimizers, Un-installers, etc installed which should be removed as per Developers Instructions. They are useless, unneeded, cause havoc and interfere with the normal operation of the OS and may even Corrupt the OS requiring a Reinstallation