This is the way. You absolutely can turn shit codebases into something nicer and faster, and this is best done by people who know the system, and maybe even more important, knows the operational context the system exists in.

I once came into an old codebase like this as a junior, thinking I can start again. And I was gently but firmly told by my boss that it wouldn't work, this software is crucial to operations that support all our revenue, and while it can be improved it has to keep working. And we improved the hell out of it.