Humans never started to eat meat. Humans and their ancestors always ate meat; it was their primary source of nutrition. You probably wouldn’t ask “when did cats start to eat meat?” because it seems quite self evident that they have always eaten meat. Same with humans.
However, unlike cats, humans are omnivorous and can eat both meat and certain plants. However, plants have always been a secondary source of food for them.
Some people lived around places that got snowfall most of the year. And we all know there were no refrigerators so storing vegetarian food was out of the question. What they did was, they started to make their living by raising cattle and that was necessary.
Also meat is a preferred source of nutrition for humans is that it is nutrient dense, unlike vegetables. That means that by volume it contains more energy, macro-nutrients and micro-nutrients than any other food source. It’s really that simple. That doesn’t mean we shouldn’t eat plant foods, and humans have always done so, simply because it’s easier to gather than it is to hunt.