Reboot, or open the Task Manager (Ctrl-Shift-Esc or right click an open area of the Task Bar) and forcibly close EoCApp.exe if it is still stuck in memory from the crash.

Try exiting out of the Steam client, and starting the game directly from the '..\SteamApps\common\Divinity Original Sin 2\DefEd\bin\EoCApp.exe' program file, by right clicking and running as administrator.
Also try starting the launcher directly from the '..\Divinity Original Sin 2\bin\SupportTool.exe' executable.

If the launcher doesn't start from the executable, try deleting the config.xml file in the '..\SteamApps\common\Divinity Original Sin 2\bin' folder, as well as 'C:\Users\<UserName>\AppData\Local\LarianLauncher' (copy and paste %LocalAppData%\LarianLauncher into Windows Explorer to quickly open that folder).
After that, try verifying local files: in the Steam library, right click on the game and select Properties, switch to the Local Files tab and then click on the 'Verify Integrity of Game Cache...' button.


If you get the launcher starting, but the game does not:
If applicable, disable Steam cloud support either globally (in the client click on the Steam menu and select Settings, and then Cloud) or just for this game (in the library right click Divinity: Original Sin 2 and select Properties, then switch to the Updates tab and check the Steam Cloud section).
Alternately, exit out of the Steam client and just start the game directly from the executable when required.

Next, try browsing to the '..\Documents\Larian Studios' folder and rename the 'Divinity Original Sin 2 Definitive Edition' subfolder.
This folder contains the saved games, configuration files and a level cache folder. Deleting or renaming it will get the game to recreate it on startup; playing the game from a different Windows user account would effectively do the same thing. With Steam running and cloud support enabled, the client would just download the cloud copy of your existing profile.
After that, see if you can start D:OS 2 DE. If so, create a new profile and maybe check that you can start a new game and save/load. If that works, exit and copy a couple saves from the renamed folder into the newly created profile's ..\Savegames\Story folder. If that continues to let you start the game and load the saves, move the rest of the saves over.
If the game still crashes, delete the new My Documents D:OS 2 DE folder and rename the original back again.