Yes it's true there is no global variables on this Event Sheet.
This is not what I said! It doesn't matter in which event sheet your global variables are defined.
I meant you need to run the game in Debug Mode and check your global variables - Levels, Experience etc. You should be able to see if they contain default values, or if the values loaded from Local Storage.
I think the values are loaded correctly, but you are checking them too soon. It takes some time to load data from Local Storage.
If you can't figure out the issue, please post your project file.