It's pretty rare for anyone to be hired into a Google/Facebook at Staff Engineer or above. (Indeed, while I was at Google they stopped hiring anyone in for Senior+, after a number of problems with "downslotting" where they promised roles to people who didn't perform in those roles.) The idea is that there is so much proprietary technology in any big company, and so much tacit cultural/relationship knowledge, that success at any of the higher levels is far from assured. Instead they were hiring in at SWE3 but with financial compensation competitive with your previous position, with the expectation that if you're good you'll rapidly get promoted to the appropriate level, and if you're not you'll leave.

Staff engineer is also a pretty high-up level. Not sure exactly what your responsibilities were at Intel/Cisco, but at Google Senior Engineers regularly take tech lead & architectural roles. Staff engineers do this + first-level management responsibilities, while Principal was roughly equivalent to what a Director would be. I'd heard (from a coworker who was the youngest person to make Director at Oracle) that Director at Oracle is roughly equivalent to Senior SWE at Google, thanks to title inflation.

Hell, I left Google for what's either "CEO" or "unemployed bum", depending on how you look at it. IMHO the idea that you could have a monotonically-increasing career path died in the 1980s; everyone I know in upper management took several steps backwards to get there, usually joining or founding a startup as an individual contributor, spending time as a consultant or EIR, switching industries, or going unemployed until someone in their network tapped them for a new role.