The game kicks off at 11. I would highly recommend planning on getting to the Superdome early. It won't be sold out like a Saints game, but it will take a while to get in. Security is strict and also New Orleanians are never in any kind of a hurry...ever. Including security guards at big events. Also, there's a clear bag policy at the Superdome that they're adamant about, so if you're traveling with people bringing purses, make sure they know that in advance.
Champions Square is probably going to have something fun going on. That's the tailgate area adjacent to the Superdome. In fact according to the Sugar Bowl website, it appears they're calling it...Tailgate Town?? lolz.
https://allstatesugarbowl.org/sports/2022/4/6/tailgate-town I'm going to try to get to Champions Square aka Tailgate Town aka Super End Zone Sugar Fun Zone probably around 9:30, maybe head into the stadium at 10:15. I'll have little kids with me though, so you could probably push it until 10:25, but I wouldn't go any later than that if seeing kickoff matters to you.