How do I add a game?

You can in Support Hub: https://www.speedrun.com/knowledgebase/supporthub/request-game-or-series

whats the general turn around time for submitting a new game, and it being added? Is it usually the full 4 weeks, or does it usually happen sooner?

@Thee_Deadguy, from @starsmiley, who reviews the games requests: