An ex-friend of mine is a lead animator & rigger for a company directly affiliated with Pixar, a lot of their 'second level' work gets sent to their studio when they get bogged down on a large project. He was discovered simply by making short films and uploading them to various animation websites long before YouTube was even around. I remember him drawing these anime related pictures back in grade 5 that you would have sworn were done by a seasoned artist... he is that good.
From what I gather, you need to have a mind blowing portfolio and be one of those 1 out of 100,000 artists who stand out. If your work is just average then frankly you don't stand a chance to became an animator with one of the big studios. Those people are looking for the best of the best. A lot of them have multi-year degrees and diplomas from art schools. My friend was self taught with Maya and 3D Studio Max, two of the most common programs for animation but the company still made him attend a college arts program.
I think with most of the arts, whether it's drawing, acting, writing or singing, it's a healthy dose of luck, determination and raw talent. You have an advantage though with YouTube and social media! If you can get a portfolio going and get a large online following to help get your content out there than you stand a better chance than anyone else. Let's face it, you're not going to be able to send a couple dozen drawings to Pixar when a job opens up and hope you get it ... there will probably be 10,000 other applicants. You need to separate yourself from the rest and just hope someone important sees your work.
It's not impossible, but close enough... :)