How can I install a non-notarized application that is not in the App Store and not from a verified developer?

Is there a possibility to install software that was not "notarized" for macOS Catalina? I have an application that worked on macOS Mojave but cannot be installed anymore on macOS Catalina. I think the developers must "notarize" this software. Checking with spctl -a -vv my.app confirmed that it is rejected.

  1. What can an end user do about it to install it anyway until this process is finished?

In macOS 10.14 and 10.15, when an app fails to install because it hasn’t been notarized or is from an unidentified developer, it will appear in System Preferences > Security & Privacy, under the General tab. Click Open Anyway to confirm your intent to open or install the app.

See Safely open apps on your Mac from Apple Support.