Large populations need large, stable sources of food. There's a reason that Arctic peoples like the Inuit who subsist on marine mammals and fish always lived in small bands thinly scattered across their territory - their food supply never supported anything more. The same is true for every known human culture that did not depend significantly on grain sources (whether wild or cultivated). Small bands were the rule everywhere that did not have agriculture or its near-precursor. You only get significant population concentrations (towns, cities, etc.) when grain supplies become reliable enough to support them.
Sure, there are plenty of animals that don't depend on grain, and people can eat them. Pigs, deer, fruit and insect eating critters of various sorts are all good eats. It's just that, unless you can guarantee these animals a sufficient and stable source of high-quality nutrition to keep a lot of them well-fed and breeding rapidly, you're never going to be able to support a big population.
And without a big population, technological civilization becomes
extremely difficult to sustain.
Do I need to add the obvious, that whenever we eat meat from whatever source we're consuming energy that originated in plants, just processed 2nd or 3rd hand through our dish-of-the-day? When the plant energy is inaccessible and the animals are abundant (e.g. in traditional Inuit culture) it makes sense to do it that way. Otherwise, it's just not that efficient a way to make food happen. In a regime of scarcity you don't want to depend for your survival on inefficient production.
Grains of various sorts became the main food source for most human cultures because they provide a reliable and concentrated supply of calories and protein and could be adapted to local growing conditions. This is a prerequisite for large population. If a massive population crash and reversion to small-band subsistence lifestyles is acceptable, ok. Skip the grain agriculture.
Otherwise, what you want is better grain crops. And hardy pollinators. And maybe some backyard chickens and guinea pigs for Sunday dinner.