You should checkout ProtonDB whenever you have a problem. Here's a direct link to the Witcher 3: Wild Hunt which is the only listing they have for Witcher 3: https://www.protondb.com/app/292030

It looks like the launcher is the problem, if you go to the game properties menu by selecting the game and pressing the 3 bars button, then under the General tab there's an option called LAUNCH OPTIONS. In the Launch Options box simply add: --launcher-skip

If there's already anything written in the Launch Options box, for example, it might say gamemoderun %command% or something along those lines, you should probably keep those there and just add --launcher-skip to the end.

On my PC running Fedora I had to manually kill a process called "DX Setup" after that it finally started compiling the vulkan shaders and then the game started.