How can I download macOS Catalina on a 2011 Mac mini that doesn't support it?
You can use Dosdude1's Catalina patcher to download the official Catalina installer from Apple's servers.
Disclaimer: I'm not a fan of bodging macOS to work on unsupported platforms, especially for &quot;production&quot; machines.  However, if you're looking to tinker and this is something to experiment with to learn, I say have at it.  If you need the latest OS for work, get a machine that supports it.
Basically, what you're going to do is trick macOS and ultimately Apple's servers into believing that your machine is capable of running Catalina so it will download.
When you run the Patcher, make sure you uncheck &quot;Auto-apply Post Install Patches&quot; found in the Options menu.&quot;  This is because you're not installing Catalina onto this Mac; all you want to do is get the installer so you can create the USB Installer.
Once you will get to a screen where you can either browse for an installer or download a copy, select the download option.

Download the DMG, it will be approximately 7GB. From there, you can make your offline installer.  The Terminal command is as follows:
sudo /Applications/Install\ macOS\ Catalina.app/Contents/Resources/createinstallmedia --volume /Volumes/Catalina --nointeraction

If this worked out for you, I encourage you to buy him a coffee or a beer (or maybe even dinner) by sending a donation his way (I'm not affiliated, I just appreciate people's hard work).  You'll find the &quot;donate&quot; link on the software download page.