Boot ROM Version: 1037.40.124.0.0 (iBridge: 17.16.11081.0.0,0)
Our new Mac mini (purchased june 2020) worked fine out of the box using Catalina 10.15.4.
We are connecting via HDMI cable.
In the first hour of use, it wanted to upgrade to 10.15.5 , so we did.
After that upgrade, the splash screen went purple at the first boot, and a purple hue stayed.
The solution in post #7 of this thread fixed it.
Thank you so much to the people who share this kind of knowledge!!