The Mac mini graphics is part of the Intel CPU, and behaves differently from the separate AMD GPU used on other Macs. Some display configurations that the Mac mini specs say should work (and do work on other Macs) don't work properly on the Mac mini. That your display does work initially when booting, then stops, indicates that the display and adapters are all working, and there is a software problem, probably with the Intel graphics driver. Are you running the latest Catalina (10.15.3)?
Since your Mac mini is new you can try Apple support, but they won't be too enthusiastic about supporting such an old display, and non-Apple adapters. It may be worth getting the complaint into their system, though.
I bought a Mac mini last year and was planning to use my old (2001) Apple display, but it would not work, even with the correct adapters. I ended up buying the LG UltraFine 4K Display
https://www.apple.com/shop/product/HMUA2VC/A/lg-ultrafine-4k-display
and am very happy with it.