1st thought... Run!

Well, I've heard you have plenty of experience with Unit Testing and TDD. Perhaps designing a few tests before refactoring?

I've heard of Snapshot testing, but have never tried it: https://github.com/spatie/phpunit-snapshot-assertions

Also, what kind of refactor are you trying to do?

ok, sounds like a 'large' project to me. Is it more an API (more oriented to developers), more oriented to UI/UX/Frontend? Perhaps both?

I'd go with prologic's advice of measuring and prioritizing. Perhaps you have a budget or at least something like "let's see how far can we reach in 6 months", and possibly you won't finish in the time you have (just guessing).

Something that has helped me was defining "Why do you we want to refactor this project?". Could it be to make it compile on newer versions, or making it easier to grow and scale, or perhaps they are trying to sell that product to another company. Every reason has a different path, IMO.