Growing a carrot???

Lol so my daughter came home from preschool with a carrot planted in a small cup with soil. We’ve been taking care of it and it’s really sprouted some greens probably about 4-5 inches out of the soil. My question is, will we be able to grow a small carrot? Or will it not actually grow in the small cup because it needs more room? I’d rather not try to replant it but she’s been excited taking care of it and I know it’d be cool if she saw she grew an actual carrot.