When raspberry pi wont boot when not connected to an HDMI output, it may be a little stressful. This happens especially if you with to connect to the raspberry pi using a remote desktop software such as VNC.
The solution to such a problem may be to simply modify a single line of code in the config file as shown below
Add hdmi_force_hotplug=1 to /boot/config.txt
The Pi4 (problem mainly persist in Pi4) will be running headless, and will be accessed via VNC.