I FINALLY get far enough without the cookie and go figure, the battle coliseum is in beta testing! What the crap!
Regardless if it's in testing or not, she would have given you the event that said that she challenged you, and you'd be able to fight her when it's open.
It's a chance that she will be added as a challenger if you make it through without a cookie, not guaranteed :).
💖 ✨ 🤗
Edit because I can't sing and coherently type.
Good luck getting her and hopefully it opens again soon.

Are you sure you reached Mama Mush? It's possible to be sent back to the beginning by a polar bear in the image other than Mama Mush, I learned that the hard way after celebrating for a few minutes....
, oooooohhhhhhhh I thought the image didn't matter, because I never saw the actual mama mush in the picture and I have done it at least 100 times.