I'd start with writing tests. That way you're more likely to notice if you break something in a distant part of the code.
Also see if you can make a to-do list. This will help make your request concrete to management. As you cross items off it will help them see that you're actually getting work done. And, it could help to motivate you if you feel like you're "just rewriting the code".
Do it.
Gradually.
Rename. Simplify. Reduce. Enhance. Test. Slice and dice.
Embrace the shitiness. Accept it. Own it.
It's your playground. Sharpen your skills, and lead them to the promised land.
It could be worse. You could face major resistance and people issues. Appreciate it.
This is an opportunity for you to kick a billion miles of ass...