Getting into a web/Big Data companies?

Find a skill you do have that is in-demand by one of those Big Data companies, leverage it into a job, and then once you're in, learn everything you can.

That's what I did. I wanted to get experience scaling programs up to massive data sets. It is hard to get a job doing that unless you've already had a job doing that, so I learned frontend web development really well instead. Most big data companies need some sort of GUI visualization or UI programming, and that skillset does not coexist very often with big-data crunching ability, and so companies in that area are often desperate for frontend SWEs. Then once you're in, it's easy to start asking questions, looking at code, and looking at how web-scale systems are put together.

Good C++ experience, good algorithm knowledge (sometimes a problem for experienced programmers who don't often have to think about performance), and good attitude will likely get you a job at many companies like Facebook or Google easily enough.

Being confident and doing your homework about the company and the position, and otherwise being prepared is probably all you need, as well as being responsive and proactive with your recruiter. There's no real downside to applying - it'll give you confidence and a reality check even if you aren't given an offer, and prepare you for later interviews.

Some companies (like Facebook) may allow you to choose which team you join - find that out in advance, or know which team you will be joining when you are interviewing.

Even if you don't immediately get to work on the team which does the Big Data work, most good companies will allow you to move around once you have proven your skills and fit, especially if you show a strong interest, speak to the right people, and contribute.