From my experience, and based on people I know that work at Facebook, e.g., getting your foot in the door is just a matter of studying medium/hard-level problems on Leetcode (speaking verbatim here). I'm not sure you need a strong foundation in systems programming or design, or even a strong track record of building great software to get hired at these kinds of companies. The metric is mostly Leetcode; it's for efficiency I guess, because of the sheer number of applicants.
I've also worked closely with a few people from such companies. I'd say only one was a great engineer. And he definitely didn't have a high opinion of his former co-workers.
The one company whose engineers I'd probably give the benefit of the doubt would be Netflix, because they're so intentional about "performance".