There is a great misconception that Mesolithic people just went into the forest and hunted and gathered food. All of those societies had not only clear division of labor, allowing for those activities on a communal scale, but also had generations of developed knowledge not just of the edible plants, but more importantly of the exact location and time of year when they could be gathered, or game could be hunted. The hunting and gathering a lot more closely resembled farming than what we would associate with someone walking into the forest and trying to feed themselves. There are still communities which largely depend on hunting and gathering. Virtually all of them depend not just on knowledge of what is edible but exactly when and where the animal or plant can be obtained. A particular fish may be available in a specific river only one week during the year, and the following week it will be in a different part of the river, or in a different river all together. A particular bird might be available for an extremely limited amount of time. Same thing goes for plants. Those early communities, much like the ones today which live in a similar manner greatly depended on knowing exactly where each plant grown, when it grows, where and when particular animals travel, feed and reproduce and then made a dedicated communal effort to gather and preserve those resources during the short windows when they are available for the rest of the year. This is not general bushcraft knowledge or knowledge of what is edible. It's easy to talk about migrating to find food, but unless you know exactly where you are going, it will be of no use.
It is possible for a person to do it these days if they are lucky, and if they have prior knowledge of exactly where the food resources will be and have it mapped out depending on the time of year. As others have also noted, certain disregard for the law is also required.
I'll also add that these days our perception of available food has been skewed greatly by agriculture and farming. "Wild" food is much more available today than it ever was. Most of the plants and animals that we look to as being abundant would be extremely hard to locate in an actual wilderness. You can hunt rabbits next to a farm indefinitely. Try finding a rabbit in the actual forest, away from any agricultural land. If we are going to talk about surviving through foraging, I say the area where the theoretical foraging is to take place should be wild enough so that it takes less time to gather the food than it does to walk to a supermarket and buy it.