63 karma · joined August 17, 2017
Every software company has these projects and many developers have been in your position. As long as the software is still functional and is profitable then management don't care how bad things are under the hood (try explaining it to someone who only sees a working/functional UI). The fact a new resource (you) has been assigned suggests it's still a valuable project.
Unless management are the ones giving the go-ahead on the rewrite then I wouldn't bother. Rewrites are very risky, time-consuming and make no money for the company. However long you think it will take...double it. You're a mid-level developer, a rewrite needs to be planned and led by an experienced senior developer.
Your best bet might be patience...try ride it out and hopefully be moved onto other projects. In the meantime you get experience. It's how you handle the adversity that could prove more valuable.