I recently joined Meta, and I'm aware of "up-or-out". However, I would like to more deeply understand how it works and have a better mental map of the entire thing in general.
How long do Meta SWEs overall take to go from E3 to E4 and then E4 to E5?
I would say it depends on the team (especially at Meta). E.g. when I was working in their AR department, managers were asked why don't they promote E3 engineers doing a great job during their 1st half at Meta. So I would say it's impossible to come with specific times.
Meta is focused on business impact and once E3 is capable to independently drive it on their feature level, deliver on time (according to their own estimates) and with a high code quality, they are usually promoted to E4.
Once E4 engineer is driving team-level impact (and not just delivers their features well and on time), they should be ready to be promoted to E5.
And the same goes with E5 engineer who starts to drive Org-level impact.
It definitely takes more time to be promoted to higher levels, but this is mostly depends on the engineer itself (as well as their team's project complexity+impact). And also it's due to the fact that driving a larger impact usually requires building more relationships, driving more challenging projects and getting buy-in from many people/teams.