I am not a lawyer, but have worked with whole bunches of them, in various specialties.
Yep, luck helps - being in the right place, knowing the right people - this helps a lot!
Also, having the right niche can be helpful - copyrights/trademarks/patents would probably be good in regions where this is especially useful (Silicon Valley, Hollywood, NYC) but the problem is, the competition is fierce in those niches, in those regions.
As an example, for an entry level position at the film studio where I worked, there were quite literally hundreds of over-qualified applicants for about 3 or 4 intern positions. Then, after about a year, they finally selected ONE intern to be hired full time - and the salary was pathetic - entry level crap. The good news is, back then the guy they hired (sort of thanks to my help) is still working at that studio and finally earing some major bucks.
The other dirty little secret about getting prestige jobs like this is just what you would expect; you have to look the part, be the part, and suck up to the right people and not be afraid to stab anyone else in the back to get to the top. Go to any of the studios and check out the new legal hires - they look like models (both male and female), but also need a degree from a prestigious school, with excellent grades. They need to work like dogs and take no credit (the other attorneys will take the credit from you), put up with long hours, sexual harassment and have no personal life. Or, you have a very close relative in the company who is a bigwig and has handed the job to you on the silver platter.
To make matters worse in prestige jobs like this, your career often has the duration of a fruit fly. Any number of factors can cause you to be fired in an instant. The minute one person is promoted, several cronies come along for the ride and others are sent packing. Keep those options open and make lots and lots of friends along the way - trust me, the day will come when you need to suddenly pack your desk and move on, and it helps to have about 200 close friends in that old Rolodex to call and see who is hiring.
My guess is, the same story is true of the big, prestigious law firms in any metropolitan city, pretty much world-wide.
Even in lowly Las Vegas, at the fairly well-known law firm where I once worked, they would get hundreds of applications for internships. Some got the internships because they knew somebody who knew somebody at the law firm But those who got in on merit worked their asses off and in the several years I worked there, they hired a grand total of ZERO of those interns. They had enough lawyers and were greedy and didn’t want or need any more attorneys.
Sorry to be the bearer of bad news, but short of hanging up your own shingle and hoping against hope of finding a few good clients, it ain’t easy.