When I hit "Play" it says that it's syncing (play turns into syncing 0%), but then just stops. I've tried reinstalling it and gog and restarting my computer, but nothing is working. I'm able to open other games on gog, so I don't think its a problem with them.

Edit: I downloaded the offline launcher and also uninstalled and reinstalled visual studio since I was having trouble with another game on epic. That seems to have fixed the problem. Still don't know exactly what caused it, but its working now. Thanks for the advice!

The discribed process is the synchronisation of cloud saves. You could try to turn it off to see if the problem is on this side.

On the other side: Does the game start without galaxy? [yourinstallationfolder]\No Man's Sky\Binaries -> NMS.exe. You won't be online in this case - just to clear the problem.

With the GoG installers, in those 4 years i had very few game crashes on start. I had 2 crashes with an error message with the Desolation update, I had to restart my computer and delete the cache files in my savegame folder (no mods installed). I think I also did a temp file cleaning on my computer.
That has fixed it, I always launch GoG Galaxy before launching the game so I get online and MP options in the game. I'm currently playing with the latest Nvidia driver 456.55.