>My assumption/prerequisite is that if you can become an immigrant, in a few situations, your family is rich already or successful back home thus you would have connections already and you're probably in mid to high economy class.

That's not always a good assumption to make. Not everyone who makes it to the US is rich or well connected. In fact, the vast majority of immigrants to the US have not been rich or well connected back home, which is why they immigrated to the US in the first place.