>show growth at Google, and if you are hired as an entry-level engineer. It isn't about what you did up to that point.

Wait, do you mean: IF you are an entry-level engineer, they want you to show growth at Google upon getting hired at Google?

What about NON entry-level? That's my point-- career trajectory is, I am told, very important to them.

Yes.

There's an expectation that if you're hired below the level of Senior SWE you will get enough promotions over time to reach that level, more or less, although as long as you show the right trajectory there isn't any deadline attached.

If you're hired right in at director level or something, it's not like you're expected to end up CEO or you get fired :)

Do you think Algorithm Design Manual is better to read than Introduction to Algorithms for preparing for programming interviews at the big companies?

I have no idea. Probably just spending some time on Wikipedia is enough. Interviewers ask algorithms questions mostly because it's hard to find programming tasks small enough to fit in an interview which cover all the basics and which aren't implementing basic algorithms.