Make sure the system date & time are set correctly. You can do this by launching the Terminal app from the Utilities menu on the menu bar and issuing the following command:
ntpdate -vu time.apple.com
If no errors, then Quit the Terminal app and try the "Install macOS" option again to see if this makes any difference.
Otherwise you will need access to another Mac compatible with an OS your Mini can run so you can use it to create a bootable macOS USB installer using the instructions in this Apple article:
Create a bootable installer for macOS - Apple Support
You can use the information in the following article to identify other Macs which are compatible with the same operating systems as your Mini.
https://eshop.macsales.com/guides/Mac_OS_X_Compatibility
FYI, it really helps to know the exact model of your Mac since multiple Mini models support Mojave....I've learned not to believe the info listed in the signature. If you have the 2018 model, then you can generally use a Mac from 2012 to mid-2019 to create a bootable Mojave installer. Or you can use any 2018 - 2023 Mac to make a bootable macOS 14.x Sonoma installer.
If you have the 2018 model and are having issues with recovery mode, then you may need to perform a firmware "Restore" which requires access to another Mac running macOS 12.4+. Sometimes the T2 chip & system firmware need to be reset before Internet Recovery Mode will work.
Edit: If you have a 2018 model, then you won't be able to boot from USB unless you can access Recovery Mode and modify the security settings using the Startup Security Utility. You must also be able to authenticate with an admin user account so if the Mac has been erased, it is no longer possible to boot to USB.