Yeah, the rules say we need a leaderboard. But you don't have to make it yourself! The hosts said that using speedrun.com is fine (here: leaderboard question - SpeedJam #1 🏎️ community - itch.io), and it looks like it's free & pretty easy to use. Plus, the hosts said you can use an "offline leaderboard", and I'm not sure what that means, but it might mean just showing the player their fastest time so they can screenshot it (but again, I'm not sure of that).
In the past though, some games have won without having a leaderboard (this one got 9th place: leaderboard question - SpeedJam #1 🏎️ community - itch.io)