Cant boot from an external device

My Mac mini 2018 supports Mojave but AFAIK newer batches might not.

Try to boot into Internet Recovery (Option-Shift-Command-R: Start up from macOS Recovery over the internet. Use this key combination to reinstall the version of macOS that came with your Mac or the closest version that’s still available). Then install some version.

Use macOS Recovery on an Intel-based Mac - Apple Support

You might then check if an earlier macOS is available via the Terminal. My Mac mini 2018 shows that as:

softwareupdate --list-full-installers

Finding available software

Software Update found the following full installers:

* Title: macOS Ventura, Version: 13.4, Size: 11511926KiB, Build: 22F66, Deferred: NO

* Title: macOS Ventura, Version: 13.3.1, Size: 11500559KiB, Build: 22E261, Deferred: NO

* Title: macOS Ventura, Version: 13.3, Size: 11500012KiB, Build: 22E252, Deferred: NO

* Title: macOS Ventura, Version: 13.2.1, Size: 12261711KiB, Build: 22D68, Deferred: NO

* Title: macOS Monterey, Version: 12.6.6, Size: 12108302KiB, Build: 21G646, Deferred: NO

* Title: macOS Monterey, Version: 12.6.5, Size: 12115811KiB, Build: 21G531, Deferred: NO

* Title: macOS Monterey, Version: 12.6.4, Size: 12116269KiB, Build: 21G526, Deferred: NO

* Title: macOS Monterey, Version: 12.6.3, Size: 12115350KiB, Build: 21G419, Deferred: NO

* Title: macOS Big Sur, Version: 11.7.7, Size: 12121126KiB, Build: 20G1345, Deferred: NO

* Title: macOS Big Sur, Version: 11.7.6, Size: 12120959KiB, Build: 20G1231, Deferred: NO

* Title: macOS Big Sur, Version: 11.7.5, Size: 12120799KiB, Build: 20G1225, Deferred: NO

* Title: macOS Big Sur, Version: 11.7.4, Size: 12119555KiB, Build: 20G1120, Deferred: NO

* Title: macOS Big Sur, Version: 11.6.6, Size: 12121263KiB, Build: 20G624, Deferred: NO

* Title: macOS Big Sur, Version: 11.6.5, Size: 12121404KiB, Build: 20G527, Deferred: NO

* Title: macOS Big Sur, Version: 11.6.4, Size: 12147782KiB, Build: 20G417, Deferred: NO

* Title: macOS Big Sur, Version: 11.6.3, Size: 12143674KiB, Build: 20G415, Deferred: NO

* Title: macOS Big Sur, Version: 11.6.2, Size: 12141944KiB, Build: 20G314, Deferred: NO

* Title: macOS Big Sur, Version: 11.6.1, Size: 12137180KiB, Build: 20G224, Deferred: NO

* Title: macOS Big Sur, Version: 11.5.2, Size: 12149332KiB, Build: 20G95, Deferred: NO

* Title: macOS Catalina, Version: 10.15.7, Size: 8055650KiB, Build: 19H15, Deferred: NO

* Title: macOS Catalina, Version: 10.15.7, Size: 8055522KiB, Build: 19H2, Deferred: NO

* Title: macOS Catalina, Version: 10.15.6, Size: 8055450KiB, Build: 19G2021, Deferred: NO

* Title: macOS Mojave, Version: 10.14.6, Size: 5896894KiB, Build: 18G103, Deferred: NO

Then download the Mojave, if available:

softwareupdate --fetch-full-installer --full-installer-version 10.14.6

Then enable external booting and create a bootable installer:

Create a bootable installer for macOS - Apple Support

Did you follow this process:

Create a bootable installer for macOS - Apple Support

No Mac can operate with an operating system that is earlier than the one it came with, whether it's installed on the internal HD or an external disk. You need to reinstall the OS the Mac came with (or a preferably newer one if possible) and then upgrade the app in question to a newer version that will work with a newer OS. If there is a cost to do so, so be it.

If these are later 2018 models then they came with Mojave. If earlier then the previous OS (High Sierra) was used.