How to make a server not joinable

So I am making this puzzle type game, and I want the servers to be limited to 4 people. Once the game starts, if another person joins, they automatically get kicked, but this has resulted in a bunch of players trying to join the game to just do the puzzle and end up joining an in-progress game and getting kicked. Is there a way to make the server no longer joinable when the game starts, so every player who joins the game lands in a server where the game hasn’t started yet?


I don’t know much about this subject but I know the API to use so I’ll just throw this out there.
There should be a good amount of youtube tutorials on teleport service and reserved servers if you need a more in depth explanation.