I am curious to why you think working at Google is reserved only for the very best of the field? I don't have good visibility into normal companies, but honestly all FAANG companies essentially employ armies of average developers, although they might have a higher density of exceptional developers than other companies. Mostly they are distinguished by two things:
* They work with economies of scale. What may be viable for a startup might be useless for Google. What might be viable for Google might be absolutely disastrous for a startup.
* They use a management style that fosters innovation and learning.
The interviews can be tough, yeah, but all it takes is practice and given that you seem to have good mathematical skills, hiding a few weeks or months in the basement with an algorithms book and a laptop, should make it easy for you to pass a Google interview.
Having spent a good deal with my of my career in the wilds of technical consulting, I can say with confidence that the product group and engineers at places like Microsoft, Google, and Amazon really are better than average. That's not to say they have a lock on all good engineers, because but they have very few bad ones.
You are right though, getting into one of the bigs isn't impossible with a reasonable amount of work studying for the interviews and aggressively seeking connections It's just that the people willing and able to do that work are already showing they have the right mindset to be a good dev a anywhere
But with these "better than average" types, what is the culture like other than constant, non-stop work?
People died to get us a 40 hour work week and here we have all these brilliant folks putting us right back in chains. They think they're getting rich, but it is all a lie. A few are getting rich, the rest are being tricked.
At Microsoft its pretty good, I can't speak well for others. Work-life flexibility is something we take pretty seriously in the groups I've worked in, and the workload is pretty manageable. It's a little >40h/week on average, but not dramatically so, and most people take their full vacation and holiday packages (3-5 weeks vacation, 12 holidays). There are bad weeks or a bad month, but its not the norm. I'd say almost everyone spends more time then that doing other technical things, but that's because we get joy out of it. Last time I tried to measure it, I'm typically doing about 5-10h/week on top of work reading technical books, researching something, or playing with some new technology on my own time.
There are also a number of true workaholics spending 60 hours + a week strictly working, but that's typically because they want to and not because the organization is running in permanent crunch mode.
* They work with economies of scale. What may be viable for a startup might be useless for Google. What might be viable for Google might be absolutely disastrous for a startup.
* They use a management style that fosters innovation and learning.
The interviews can be tough, yeah, but all it takes is practice and given that you seem to have good mathematical skills, hiding a few weeks or months in the basement with an algorithms book and a laptop, should make it easy for you to pass a Google interview.