Hi Nakade, good question! If you made a game specifically for this jam and you started/finished making the game early, you can totally submit it once the jam officially starts. If you made the game for a previous jam or are just looking to promote your latest work, I would politely ask that you not submit the game.
I'm thinking about making a supplement for one of my already-existing TTRPG's, so that way I'm promoting my own (free) work while also creating something new for the jam (a post-apocalyptic world to match the jam's theme, but also one I've been wanting to make for a while). You might think about doing the same thing... you have a whole month to work on it and it will be a good way to promote your already existing work. Just make sure you have a free "quick start rules" available so people can try it for the jam.