It's definitely possible! Cost of groceries in the outer boroughs will be cheaper, but I'll use Manhattan prices. Shopping at Trader Joes + Chinatown will significantly lower costs. Fairway isn't terrible, but if you're shopping at the local market, it's super expensive. Whole Foods is insanely priced.

Breakfast will be your cheapest meal, eggs $3/dozen. Yogurt 99c each or get a larger container to save more money. Oatmeal, bananas. Bacon will be pricey, but let's splurge $6. Avocado, toast is relatively cheap.

Lunch, chicken breast, thighs whatever. You can get them for $5-6/lb and even less at Chinatown. That'll go for lunch/dinner. Toss in salad, rice, etc. Canned veggies like chickpeas and beans are just a buck each at Whole Foods. Ground beef is pretty cheap. Veggies like kale, broccoli are a bit more expensive, but again, only a few bucks and you can use it for multiple meals.

Grocery might cost more, but definitely possible to churn out meals at $3 price points. Of course there's the upfront cost of having basic things like salt, pepper, oil, spices, butter, etc.