So when I launch the game, it shows a black screen, maybe the intro of text for a fraction of a second, then goes to the desktop.
The game is still open, and I can click on it go go back in. Sometimes it just boots me out again, sometimes it lets me play fully. I have turned off all overclocks, geforce experience, and reinstalled the game without mods. Honestly, I am stuck as to why this is happening.

System specs:

GTX 960
i5 4460
16GB RAM
Windows 10
240GB SSD (with witcher 3 installed on it)
1TB HDD

Usually I would say it's the graphic cards driver, some drivers often cause that randomly.
But since you have W10 I don't know if thats the problem maybe the OS is causeing something I don't know about (I don#t use W10)
Just try a different driver maybe it works (I'm using 352.86 but I don#t know if that one is also avaible for the 960).