It's like the situation where you submit the materials, but the case isn't filed, nor are you issued a decision about rejecting the case—basically, every lawyer has experienced this.
This kind of situation can actually be understood. In some places, grassroots courts handle far too many cases, such an overwhelming amount that they simply can't complete them within the statutory time limits.
So, they can only stall at the filing stage, letting cases queue up first. When things aren't as hectic, they'll officially file your case.
Take grassroots courts in cities like Beijing, Shanghai, Guangzhou, and Shenzhen, for example. Each judge has hundreds of cases queued up under their name. Complaining to a higher court about it won't give you any real results, because the higher courts understand the situation.
Under the quota system, judges are limited in number. They still can't finish the work even if you fire all of them—things will remain the same.