Even though we know there is no chance from an outsider to being hired by a famous studio such as Microsoft Studios, EA Games, Epic Games, etc. we keep trying. Because that's what matters. Who knows, may be one day someone from such studios will come looking for really talented foreigner programmers.
Other countries seem to think that people in the USA don't like them because people from the USA are rude and obnoxious toward them. This is not the case. We are rude and obnoxious toward everyone. MicroSoft, specifically, I know will hire anyone who they feel is the best person for the job. They don't care where you're from as long as you can do what they want. I suspect other companies are the same. There's not strong xenophobia.
That being said, the big studios in the US all started out small - even the more recent ones. They didn't just pop into existence one find day and start crapping out cash cows. They had an idea for a game and they struggled to find the resources to make it happen. Success led to success and they became giants. The same can happen in Mexico. It's hard but it can happen.