Of course, people did it years ago and nomadic. Which meant they traveled with the animals.
Example: If plains buffalo went further South in the winter, so did the Plains Peoples.
They also had small gardens and farmed in small areas during the spring and summer, foraged on natural growing fruit, and ate what was around moose, deer, rabbit, rodent.
Of course, you couldn't do this living in the city. It would take to long to grow a back yard garden you could feed yourself off of, you can not hunt legally, and there is no wild food about. But if you live near a forested area, or an area where game hunting is legal. sure, you can live off of what you can hunt for quite some time. keep in mind there are limits to how many deer and such you can shoot. Where I live it's 4-6 a season and I think tags are needed after 3? They have to be a certain sie, males only, and antler sizes has to stay under a certain measurement each year.