I had a lot of problems in the beginning trying to get Game Mode working properly, so that I had high refresh (144Hz) with VRR (variable refresh rate) to benefit running games up to 144fps on to this TV.
One thing that helped was to reinstall the NVIDIA drivers by using the Custom Install option for removing previous graphics drivers and deleting profiles, before installing the drivers for a clean install - Express install was no good. Once that is done, you then have to explore and change the settings within the NVIDIA Control Panel (not GeForce Experience). There are settings for enabling variable refresh rate, which is the same thing as G-sync.
In NVIDIA Control Panel > 3D Settings > Manage 3D Settings > Global Settings > Monitor Technology, it should show "G-SYNC Compatible"
Then in NVIDIA Control Panel > Display > Set up G-SYNC, under section 1. the "Enable G-SYNC, G-SYNC Compatible" should be ticked and the "Enable for full screen mode" selected. Then under section 2. Your external TV display should be showing as an icon and then under section 3. the "Enable settings for the selected display model" should be ticked even though the information below states that "Selected Display is not validated as G-SYNC Compatible" (just ignore this ans ensure it was ticked).
Also ensure beforehand and after that the selected resolution is set to native (3840 x 2160 for my TV mentioned in my post).
Also I have default colour settings selected, otherwise if using option for NVIDIA colour settings, I found that the Output colour depth can literally kill your connection if setting on one of the higher 'bpc' settings... It's ghosted out and unsettable (8 bpc) when using standard default colour settings, but if using NVIDIA colour settings and then changing it to a much higher value, then you may enter a world of pain trying to re-establish your connection back.
Hopefully if all is done properly and you've got a genuinely certified HDMI 2.1 cable, then you may be able to use the Game mode on the TV with high refresh rate/high frame rate with VRR enabled.
Incidently, I have all of my HDMI ports on the TV set to 'on' (enabled) for "Input Signal Plus". However I don't bother with any HDR settings, therefore HDR is off as it does not look good to me.