Don't current Googlers find that depressing?
I've also heard that pay raises within a team at Google are often designed to "level out" the spread. So if you started low, then you eventually catch up. All anecdotes and internet readings though, would love it if someone with actual knowledge commented on these things.
As for raises, that's almost right. Given two people performing equally, one who makes more than the other, the lower paid one will get larger raises, until the salaries are approximately the same. If one performs better, they'll get larger merit increases.
This is all subject to the assumptions that the system is fair at rating performance, which I try to ignore when explaining the mechanics to people.
It's not unusual to see a huge pay discrepancy based on your ability to negotiate. It also depends on what ladder you're applying to (i.e. you can't compare a Solutions engineer comp at Google to a SWE at some other company).
In fact, when you're negotiating comp, I'd argue that an additional $1 of signing bonus or starting equity grant might be worth more to you than $1 of additional salary, because a bigger signing bonus or equity grant doesn't come at the expense of future salary raises.
However, the level you start at matters a lot. If you're an experienced industry hire who should really be an L4 and somehow get slotted as an L3, you'll spend 1-2.5 years waiting for the promo to L4. During that whole time, your peers who were hired at the correct level will be progressing towards L5. This doesn't happen frequently, but it's unfortunate when it happens. In that situation, it can actually make more sense to decline the offer and re-interview to get an L4 job offer later, since that might take less time than getting promoted internally.
After I reread the things I forgot about - implementing things I was hazy on, like Dijkstra, on the way - I solved a handful of leetcode questions, read a few system design analyses, attended an onsite at a "practice company," and finally scheduled my big-N onsites. All told, I studied about 4 hrs per day for five days. But I think it's really important to be honest with yourself; this process seems to work well for me, but your ideal process might be different.
TLDR: in my current experience at non-staff levels, Google comp lags behind "Big-N" comp as well as "near-IPO company" comp. Maybe they just lowball everyone though.