Hi and welcome!
This is probably easiest made with message passing. You could also maybe use a shared Lua module, but this is what message passing is for!
Given that your script is called main and is in a game object named go (like the image)
You can then do msg.post("/go#main", "start") in your .gui_script
And in your .script you would check for it in the on_message
function on_message(self, message_id, message, sender)
if message_id == hash("start") then
-- Game should start
end
end