Your best bet would be to connect with a few folks in the talent acquisition departments at each company on LinkedIn. Once you are connected, you can follow up with a kind note asking for more information on employment opportunities and advice on getting started in those organizations. They will be able to best guide you are areas of the organization that you might be interested in working and what types of positions to look out for - as well as the types of things they look for in new hires.

Go through your network. Do you know anyone that works at FB and LI? Do your connections know people that work at FB and LI (second-degree connections)? Chances are, you have a lot more connections at FB and LI than you might think. Ask your connections to introduce you to the folks they know that work at FB and LI and then schedule 30-min informational interviews with these folks. You now have a connection at FB/LI and can ask them what it's like to work there.

My experience says - it is a waste of time in those platforms. Can be used for getting acquainted or information, but for business needs a lot of time and patience.

The first thing you do upon starting at Facebook is go to a boot-camp where you learn about Facebook internal systems, architecture, and code so you can contribute early. This is not to say that Facebook does not have, say, data scientists, but everything revolves much more around product. LinkedIn has great product focus too, but the overall mix of roles and skills is more diverse. In any case, payments are not about innovating but leveraging market position to extract shares of revenues.
LinkedIn is rather unique among leading tech companies in terms of the diversity of its business model. LinkedIn has been great in establishing leading position as an elite source of top talent. That is a great position to be in as their customers are not driven by measuring ROI but instead perceive they must participate, or they would be losing out to their competition in recruiting the best talent. On top of all that, LinkedIn revenue has been growing faster and their management of investor expectations has been just about perfect.
Facebook has been less successful, at least initially, in managing investors’ expectations, by mismanaging their IPO and initial growth expectations. LinkedIn timing for IPO was better and their current, as well as eventual prospects for growth are better. Their current market capitalization is $28B, while Facebook is at $218B. For Facebook, that would mean almost $1 trillion valuation, something never seen in history while LinkedIn would be around $110B.
Another set of differences comes from the nature of their data. Facebook's social graph is at the heart of their business, but not at the core of their business model nor even product. LinkedIn has been innovative in launching a quality news feed themselves but that is not at the core of their offerings.
Besides if you do have any questions give me a call: https://clarity.fm/joy-brotonath