I started at Disney at the end of 2015 right as they were fishing up on Zootopia, I'm one of the newest animators there! Getting into Disney was a long journey. Not everyone comes out of school with an awesome film like Mario's!
After graduating from Sheridan College in Canada, I started just by working anywhere I could and getting all the experience I could. I worked for 8 different studios (...maybe more, I lost count) before getting into the Talent Development program at Disney.
Every career choice I made came down to "what is going to make me a stronger animator?".
Over the years while going from job to job, I was also doing animation tests on the side. That was a big part of my growth as an animator. If the work I was doing during the day at my job wasn't something that I thought would get me a feature animation job (or wasn't pushing me enough creativly), I tried doing tests. And I would also try showing these tests to other animators I trusted to get feedback from them.
Eventually being persistent with that paid off. I had some professional work on my demo reel that I sent to Disney but from what I've heard they reacted best to my personal work that was 100% my own.
So I think it really comes down to working hard and trying to soak up as much knowledge as you can. Timing is a big thing that's out of your control, but luck favors the prepared! Keep animating and stay persistent :)