Can I consistently pass the technical exams? Read Elements of Programming Interviews cover to cover.

How can I get in contact with a recruiter at Amazon? Trade shows, through university contacts etc

Am I someone who is humble and likeable? This isn't talked about enough.

If you can do these things then you should be able to get a job at the big companies.

One last thing. There's so many different roles at Amazon you need to ask yourself "what am I most interested in?"