My best advice see if you can make friends with people that work at those companies. They'll be able to give you advice on how to pass the interviews, what they ask, and if you want to work there. Sarah Drasner helped me get my job at Microsoft and Derrick Showers helped me get my job at LinkedIn. Knowing someone always helps.
Beyond that, brushing up on your interview skills is essential. Being a good engineer and a good interviewee are (unfortunately) orthogonal skill sets. Cracking the Coding Interview, Code Katas, and all those things that help you reason through abstract problems quickly will help with Big Tech's silly interview process.
Hope that helps!
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