It is recommended to not make such a large leap in operating system versions, skipping more than two macOS releases is inherently dangerous. I sincerely doubt it receives the same kind of testing that an incremental upgrade would receive. Ideally, it would be recommended to backup your data and perform a clean installation of Catalina if you can create a bootable macOS flash drive possibly with another Mac.
However you can try upgrading to an intermediate version such as Sierra or High Sierra then upgrade that to Catalina. A great deal has changed and the big one is the change from JHFS+ filesystem to the new APFS filesystem.
If your disk is encrypted you need to turn off FileVault or you are going to be at far greater risk of a major problem.
Here are the Apple Support pages where you can download various versions of macOS using special links. The downloads are hidden from the App Store via search or are distributed from backend CDN Apple storage. For High Sierra+ the downloads will be made from the App Store but older releases will come from a CDN (Content Distribution Network).
https://support.apple.com/en-us/HT208202 - Sierra
This will download an InstallOS.pkg that creates the /Applications/Install macOS Sierra installer which needs to be run manually after the InstallOS.pkg.
https://support.apple.com/en-us/HT208969 - High Sierra
https://support.apple.com/en-us/HT210190 - Mojave
https://support.apple.com/en-us/HT201475 - Catalina
Instructions on how to make a bootable installation for everything but Sierra
El Capitan can be rather difficult to get working, your mileage may vary. I've found it to be far easier to go with Sierra or High Sierra.