This is all very applicable to Google. I was at Google for 2 years and I got promoted L5 to L6. The key (I think) was working across teams with people who were already L6 or higher, and who were willing to write for my promo packet.

In terms of what I learned? I think the most important lesson was: Don't get bogged down in details that are irrelevant to you & count on others to do their jobs. I came from a small (~15 engineer) company where we all knew the entire product from top to bottom. At Google, that was impossible.