I was playing No Man's Sky today, I finished the new expedition, and the game started crashing. When it finally finished doing whatever it was doing it says "Some user files previously uploaded to GOG Galaxy Cloud conflict with files on this computer. Which location has the most correct data? GOG Galaxy Cloud; Last modified: 53 years ago; This computer; Last modified: 53 years ago" First of all, I'm pretty sure GOG isn't 53 years old, i know my computer isn't, so I got a little chuckle, but will picking one of these option delete my game saves?

The 53 years thing is just the Unix Epoch; when a valid time/date can't be found, some software chooses to default to the Unix epoch.

The short answer to your question is that choosing the wrong save will result in you losing any progress you made between your last successful save and the game crashing. I would tend to assume the data on your PC will be newer, but I guess it's possible the game managed to upload to the cloud before crashing?

Edit - The smart play might be to make a backup of your local save (on your PC), to somewhere outside the save folder. Then if the cloud save isn't newer, you could still replace the local save and not lose progress.