The problem isn't just poverty, it's generational poverty. Immigration is expensive and time consuming, whether you take the legal route or not. If you managed to immigrate to another country, that's already a huge achievement regardless of how much money you'll make there.
Also even cheap/easy unhealthy food can mean different things depending on your circumstances. There are plenty of tales of startup founders living on ramen before their company turned a profit or landed the investment but their situations are very different from those of the working generationally poor.
The ramen is always a temporary thing, a cost-cutting measure on your way to becoming a millionaire (or at least falling back onto your family's safety net of free rent and food if you fail). The Saturday McDonald's on the other hand is the highlight of the week because there's literally nothing to look forward to and you're already on the last dimes of your payday loan.
Immigrants also occasionally to have support networks that born-american poor do not. Additionally, while some immigrants appear to be barely scraping by, sometimes its an improvement of circumstances compared to the okd country. That resilience is borne out of environments no American should be subjected to, IMO.