To get even more specific, do you mean ground meat as in the sort of modern ground meat or meat that has been reduced to tiny bits?

The first (known) modern meat grinder was invented in 19th Century Germany by Karl Friedrich Christian Ludwig Freiherr Drais von Sauerbronn.

Aside from just finely diced meat, Sausage is going to probably be the oldest way for "ground" meat to exist, since it has the ability to be held together and smoked, salted or dried for preservation and allows the use of more parts of the animal, adding more calories into the diet. But, the oldest reference I can find to sausage that could contain "ground meat" is a type of blood sausage mentioned in Homer's "The Odyssey".

A lot of basic foods evolved from items that don't last long (preservation wise) in their first state, cheese being an excellent example. But most of these (meatloaf probably being an exception) pre-date written history.