"De kleine doos zit vol."
Translation:The little box is full.
No, your error is not in verb tense. Your sentence is just odd English. While it's perfectly normal and correct to use "zit" (from zitten) in the Dutch sentence, in more acceptable English you would have to use is/are. Here's a good article on this Dutch grammar rule: https://www.duolingo.com/comment/5785064.
Is the use of zitten here because the unspecified objects inside the box have filled it? Or is it because a box takes zitten (in the same way that, e.g. a car takes staan or a stad takes liggen)?