So in my case, I finally found the good combination :

• Proton 4.11 max because the game run and exit with Proton 5.x
• without PROTON_NO_ESYNC the loading screen freeze
• AND I need to add a custom config file to adjust settings (and avoid a black screen)

Here is the content of my config file in steamapps/compatdata/287260/pfx/drive_c/users/steamuser/Saved Games/Codemasters/ToyboxTurbos/video_settings.xml :

<?xml version="1.0" encoding="UTF-8" ?>
<config width="1920" height="1080" fullscreen="true" msaa="false" brightness="0.500000" depthOfField="true" smoothingType="-1" VR="false" VRRenderFactor="1.000000" />

In this file I can adjust my screen resolution (1920x1080) but I also have to set MSAA (anti-aliasing) to "false" : this solve my black screen problem. Note that if I re-enable the anti-aliasing into the in-game options, the game freeze... so I need to keep MSAA false and the game finally works !