I believe startups should implement levels once you hire 2 engineers. It's hard to retrofit a system, especially if you're trying to be thoughtful about any pay imbalances.
There weren't necessarily 6 levels of hierarchy (below the L6 staff). It's almost certainly for hiring purposes - to tell hires that their role is similar to that of a Staff Software Engineer at Google (i.e., L6). Like many things in tech, other companies tend to base their leveling system after Google, and you can literally put companies side by side on https://levels.fyi to compare per-level compensation at different companies.