I'm new to this and want to see how I can set up a submission for one specific game (Cars Mater National) but for some reason, every time I select Submit Run it comes up with an error saying I need to sign in first when I am already signed in. When I try and submit run for any other game it works fine but not Mater National.

Could you try to resubmit your run again to Cars Mater National? I think because you tried to submit a run the second you created your account it bugged / got stuck in the cache. Or try a different browser just in case. If the same error pops-up, it is the best to report it in the bug report thread: https://www.speedrun.com/The_Site/thread/onfz6