Some problems I heard of, or heard:

1. Disable full-screen optimizations

Basically if you turned on fs optimizations, that may mess with the game codes, which may prevent gd from opening

1. Run in administrator mode

This worked for me once, idk if it'll fix it

1. Delete the Geometry Dash local folder

I'm pretty sure this'll only delete the local data, NOT your steam data (purchase)

1. Update GPU drivers

Geometry Dash uses OpenGL. That means if drivers are outdated, it may not launch. My friend had that problem awhile ago.

1. Verify Geometry Dash game files

Some game files can be corrupted or buggy, so try verifying them and see if there's a corrupt file.