Hi there,
As far as I understand, SEO ranking is based on your URL so you shouldn’t lose the ranking if the URL didn’t change.
I would start a staging site and duplicate your existing site over, activate GP in the staging site, make the tweaks there, then push it live once it’s ready.
There should be lots of articles/resources on Google providing instructions on how to switch theme as well as it’s not a theme specific question.
Hope this helps 🙂