I have strong feelings on this, so rant imminent. I also want to preface this by saying that these are my feelings and not necessarily representative of the entire community as a whole, in case that gets misconstrued somehow.
I've decided that what I do is for two groups:
That's it. Notice no company is any part of that. Now, if in trying to accomplish these tasks for #1 and #2, I can benefit a company, so be it.
Say I wanted to work for Google (which I don't; a search engine front which uses peoples data is of no interest to me), Facebook, or any number of large company. Before I even go there, I know one of several things:
The above would be my overall expectations when I put that application in. Now, there's a chance these bad things won;t happen and it'll "all just work out" but this is life, it's not a TV show and we all know how life is.
You have to remember that the creators of these said companies all got rejected from other companies. In fact in some cases, that's the reason why they started their own. A big company rejecting you basically says nothing about you. Now, if you kept getting rejected over and over by everyone for years, I would say step back and look at what you're doing and/or how you're presenting yourself... But otherwise, keep learning, keep coding, and keep applying.
Not sure why anyone wants to be a farmer in the zillions at these huge companies, aside from pay and benefits, but that's just me. I personally don't want to be a bot, I want to have a bigger impact on my workplace than to be employee #478237 from Engineering. But not everyone is me and I respect that.
Another perspective that I want you to consider is that large groups of people are often all wrong. There's this strange misconception that "the more geniuses under one roof," that they are mysteriously right all the time. This is completely false and it has been proven time and time again when aforementioned smart people will invent or create something that the 20,000 geniuses at Microsoft and/or Google overlooked. The reason this happens is because although Microsoft and/or Google employs said number of very smart people, not all of them are given the authority to use their smarts. I could be Team Lead of Windows Operating System for example and perhaps I haven't thought of something. Joey from my team has only been there a year and frankly, he has a better idea than I do and than the stakeholders do. However, company politics and policies prevent this idea from going into place. We've now displaced the fact that we have Joey, smart guy, on the team. Does this make sense? Large companies start out free/open but end up walling people in. When you wall geniuses in, their effective smarts diminishes. Such behavior can be seen, when, for example, a 16 year old stumbles upon a way to break Windows login and the bug has existed for 15 years without anyone at Microsoft knowing.
I invite you to consider that fact and use it to better situate your mind when you get rejected by a big company. Cheers,