I actually got the same problem with my Belkin VR Cable and PC. Motherboard is a bit older (forgot the name, CPU is 3770k), GPU is a RTX 2080. Display wont start on a fresh boot, reconnecting the cable on the display makes it turn on immediately.
Do you think a HDMI Dummy Plug might make it work since Legetrekt „fixed“ it by connecting a different display as well via hdmi?
The dummy plug is typically for situations where for whatever reason the display driver isn't getting initialized at startup. It tricks the PC into thinking a display is attached. In lelgetrekt's case, it sounded like the BIOS or something was not seeing the ASD as being attached at startup which is why I suggested it. They also make DisplayPort dummy plugs for the same purpose. The easiest way to see if it'll help is by hooking up another monitor or TV to the hdmi port. If it results in the computer starting up correctly and showing the login on the ASD, then you can use a dummy plug.