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.
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.
Cooking requires both time and resources. Most healthy ingredients have a limited shelf life and are bulkier (low calorie density) so you need to do your shopping more often. You then need to store them so they don't spoil too quickly (which is harder if you have a small kitchen and no pantry). Then you need to prepare meals in advance and cook them, both of which requires not only dedicated time but also time available on a somewhat predictable schedule, not to mention making meal plans in the first place to organize your shopping, which not only takes time but also mental energy.
Compare this to simply stocking up on cheap meals and throwing one in the microwave for a few minutes at dinner time.