Years ago, I thought, "Why would I want to bust my butt to join Goog or similar and be a cog in a giant machine?" It seemed to me like you try hard to prove yourself to get in just to be on the bottom of the totem pole where being recognized would be very hard. So I didn't bother and worked at other smaller companies.
In retrospect, it seems like your best move in the Valley IS to just try to get in to the biggest, best name, with the most talent flowing into it. IF and when you want to leave for somewhere smaller (or start your own), you'll be well served for having done it, networked, gotten the resume boost, etc.
So while yes, it may be true that the updraft opens up spots, maybe if you get one, you'll be looking back and seeing that during those years, having Goog or similar on the resume will not be as boosting to your career as Uber or AirBNB et al.