Displayport to hdmi cable goes no signal in ubuntu after 10 seconds

I bought a Displayport to HDMI cable to use my second monitor, on my b660 plus asus motherboard which has a displayport along an hdmi port. I also have igpu on cpu (intel 12400). When I connect my both monitors separately through HDMI, there is no problem everything is good. But when I connect a single monitor via Displayport to HDMI cable, I have screen for maybe 10 secs, then the screen goes black (with "no signal" message), then unplugging the DP cable won't even get the screen back for that short period, but unplugging the power cable along DP cable, and plugging both cables again would give us back the screen for that short nearly 10 seconds period.

I have no idea why this issue happens in this form for my device, I should also mention that when I plug DP to HDMI only, and navigate to BIOS, I have screen with no problem there, as soon as I exit the BIOS, my screen again goes black even in the boot section.

No LSB modules are available.
Distributor ID: Ubuntu
Description:    Ubuntu 20.04.6 LTS
Release:    20.04
Codename:   focal

*-display                 
       description: VGA compatible controller
       product: Intel Corporation
       vendor: Intel Corporation
       physical id: 2
       bus info: pci@0000:00:02.0
       logical name: /dev/fb0
       version: 0c
       width: 64 bits
       clock: 33MHz
       capabilities: pciexpress msi pm vga_controller bus_master cap_list rom fb
       configuration: depth=32 driver=i915 latency=0 mode=1920x1080 visual=truecolor xres=1920 yres=1080
       resources: iomemory:600-5ff iomemory:400-3ff irq:180 memory:6002000000-6002ffffff memory:4000000000-400fffffff ioport:5000(size=64) memory:c0000-dffff memory:4010000000-4016ffffff memory:4020000000-40ffffffff

Screen 0: minimum 320 x 200, current 1920 x 1080, maximum 16384 x 16384
DP-1 disconnected (normal left inverted right x axis y axis)
HDMI-1 disconnected (normal left inverted right x axis y axis)
HDMI-2 connected primary 1920x1080+0+0 (normal left inverted right x axis y axis) 598mm x 336mm
   1920x1080     60.00*+  74.97    50.00    59.94  
   1680x1050     59.88  
   1280x1024     75.02    60.02  
   1440x900      59.90  
   1280x960      60.00  
   1280x720      60.00    50.00    59.94  
   1024x768      75.03    70.07    60.00  
   832x624       74.55  
   800x600       72.19    75.00    60.32    56.25  
   720x576       50.00  
   720x480       60.00    59.94  
   640x480       75.00    72.81    66.67    60.00    59.94

It is really odd that in the short 10 seconds period when I get the output of xrandr command, I see the DP connected monitor in the HDMI-1 part above.

I would be grateful for any kinds of assistance, since I'm struggling with this frustrating issue for a couple of days.