I see many strange statements in your text. The choices of a freshman aren't permanent. You can always go back an change your degree program; it just may take longer. A friend of mine in college decided in his 5th year of engineering (it's a 5 year program there) to switch to physics, so he was in school for about 8 years. Even if UW says that you cannot change majors (very unlikely), you could always switch colleges. The question of course is where your money comes from, but you didn't say that was a big issue, only a parenthetical one.
Second, you didn't say anything about getting a minor in CS; why not? What's preventing you from taking CS courses anyway? Even after you fulfill the CS minor requirements, take a couple of extra. That would also indicate to prospective employees that you are interested in learning things even when it isn't required.
Third, I took too much math in college. My math department let people fulfill either the pure track or the applied track. I did the pure and most of the applied. I can say that the calculus of variations has never ever been useful for anything I did later, and what I learned most from Principles of Real Analysis II was that I wasn't interested in pursuing real analysis as a career. Oh, and "Groups, Rings, and Vector Spaces" was the only C I got in college. Taking that class could have been useful if I decided to go into particle theory in physics grad school. I instead went into biophysics.
In some sense we are all autodidacts, it's just some of us have more direct help than others. Sure, you could figure out most of this on your own, but it really helps to get help from others when you are stuck, or to get a sense of which problems are important, and to learn what's new vs. what's well-known.
As for working at Google, MS, etc - you do realize there are many positions at those companies, right? A friend of mine dropped out of school as a film major, did some work helping out with local GIS companies, moved to the Bay Area to work with a GIS software provider, then GIS at Autodesk, and is now Lead UI Designer at Microsoft Games. What you major in can help you advance faster on your career path, but that's only if you know what you want to do. As you don't, figure out what it is you want to do, and in the meanwhile, finish off your BS in math/CS minor while talking to people about options.
Hint: "work at Google" is not a good career goal. After all, what are you going to do after you are hired by Google? Another hint: don't you have an advisor you can talk with?