I had the same problem, when i started the game i got a blackscreen after the logo of larian.
Here is the solution that worked for me with NVIDIA.
-go to : NVIDIA Control panel > Manage 3D settings > Program Settings In "Select a program to customize:" choose DOS2 and "Add" then make sure that in the option "Select the preferred graphics processor for this game:" is set to "high-preformance NVIDIA processor"
-Now open your file explorer and go to : " \Program Files (x86)\Steam\steamapps\common\Divinity Original Sin 2\bin" and open "EoCApp" as Administrator (Rightclick "run as administrator")