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.