I’d keep it a mystery, but imply he’s been alive well over 500 years, if not substantially longer.
If I had to give Palpatine a backstory, as much as I liked his characterization in the Darth Plagueis novel, if it were up to me, I’d probably go with the “ancient being” angle. Have him be this eldritch, demonic entity where no one knows how long he’s existed.
Maybe he could be the one who ruled the galaxy 1000 years before the movies?
That’s an interesting angle too.