I have interviewed with two "Big Corp" companies and during the interviews I asked about the possibility of an immigration sponsorship considering that I live in a South American country, and they have always assured that once the interviews are done and the company extends a job offer they can help during the immigration and relocation, not only to North America but also Germany, Scotland, Japan, Canada or any city where they have an office.

I wouldn't worry about that, just be sure to study a lot to improve your profile as much as you can, every skill counts considering the fact that they receive tons of resumes all the time, you have to differentiate yourself from the others.

PS: Since you mentioned being a front-end developer, I want to give you some advice with respect of your current learning strategy. A couple of days ago I interviewed for a position in the web development team of one of the "Big 4", my background is mostly on back-end development. After reading several articles from people who interviewed with the same company I realized that most of the questions they were asked were related to algorithms and data structures, so I decided to refresh those skills, bought the latest edition of the CtCI book. The day of the interview I was surprised to find that all the questions were regarding the DOM, basic CSS concepts, and new features introduced in the latest specification of JavaScript. During the ~40 mins of the interview I was never asked one single algorithm question.