[NonEUCitizen]

There is also the "green card lottery" for those in countries where fewer immigrants come from:

https://en.wikipedia.org/wiki/Diversity_Immigrant_Visa

[quantumofalpha]

Chance of winning is under 2% for almost all countries and it's not particularly fast - apply in November, learn in May whether you can immigrate from September.

Regular H1B would be both faster and offer a better chance of winning.