(***2023 EDIT:***)
This guide was made over 2 years ago, but as per several comments the game's physics like other games is tied to the FPS so things can get really wonky when adjusting this. In order to fix this MAKE SURE to use the High FPS Physics Fix for FO4 from Nexus.

Link: https://www.nexusmods.com/fallout4/mods/44798?tab=posts

Guide:

This fixes the black screen upon launching Fallout 4 on 300hz monitors where audio is played but the screen is black

5 Minute Video Version: https://www.youtube.com/watch?v=AnSSTnAdYBM by G Money

Open up your file explorer and go to:
Documents > MyGames > Fallout 4 > Fallout 4 Prefs . ini

in the ini editor find "iPresentInterval=1" (Use Ctrl+F to find this text easier)

Set this instead to iPresentInterval=0

This uncaps your game's framerate and allows the game to get un-fücked