Good on you for pursuing continued education.
Yes it's viable - never lose hope in yourself for anything. The Brain Residency has no age requirement; in fact, the program looks for diverse academic/career experiences. You'd be surprised how close you are to your dream job if you are passionate, hardworking, and lucky.
I too, was intimidated by the math & magic of ML when I first took Andrew Ng's Intro to Machine Learning Course 4 years ago (my first exposure). I took regular CS courses in college and started focusing on ML 1.5 years ago. Beyond taking courses, I highly recommend building your own projects - it exercises your independent research ability and creativity.
The Brain residency pays a good wage for the SF Bay Area (comparable to new grad salary at average tech firms), so you should be able to pay your bills. I've heard rumors that many other companies highly invested in ML are following in Google Brain's example and starting similar residency programs. Your ML career path need not be at Google, though we're a pretty solid choice ;)