according to the guide:

https://support.apple.com/en-us/HT201372

I tried to make install USB stick and install High Sierra on Mac mini 2009.
As I remember It had High Sierra. But it does not continue after choosing the install USB stick as booting disk. An error icon appears.
Then I found that the newest OS for Mac mini 2009 is El Capitan.

But El Capitan cannot be obtained from App Store.
I found a link to download InstallMacOSX.dmg for El Capitan: (This can be dangerous. But I guess macworld is a trustable site.)

https://www.macworld.co.uk/how-to/mac-software/install-old-mac-os-3679956/

https://www.macworld.co.uk/how-to/mac-software/download-old-os-x-3629363/

Then I have to install InstallMacOSX.pkg in InstallMacOSX.dmg, but it does not work in recent Macs.
Luckily I have a Macbook Pro 2015, and it can be installed on this macbook.
Note that this installs OS installer, NOT OS itself.
And then "Install OS X El Capitan.app" is installed in /Applications/ and run this app to make a bootable USB install drive.
$ sudo /Applications/Install\ OS\ X\ El\ Capitan.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume --applicationpath /Applications/Install\ OS\ X\ El\ Capitan.app