Answer: You can try practicing rhythms and practicing your music in general. You can also scan the page and identify anything familiar and unfamiliar to you.
Explanation: Just an FYI, I am talking from experience in concert band, but I think these tips would still apply in some way.
The more you practice different rhythms, the easier you can recognize them. Practicing music in general can also help you with rhythms and notes. Knowing your scales and different intervals such as perfect fourths and fifths beforehand can also help you "hear" the music in your head before you sing as well. When you do receive the music you must sight read, it is good practice to scan the page for time signatures, the key signature, tempo, and find any repeats in the music, if any. Scan the page for any parts that seem difficult to you, and try to practice them a little in some way before you do have to perform it. If it is still difficult to you, then try taking the piece a little bit slower to make it more doable. The judges probably won't expect you to perform it perfectly up to tempo.
I also recommend Sight Reading Factory as a way to practice your sight reading because it also helped me when I was in concert band. I think it will help you too.
This explanation was a bit lengthy, but I hope it helps you and I wish you the best for your audition!