According to the mainstream scientific view, the Palaeolithic or old stone age began some 2,000,000 years ago when stone tools began to be used by hominids such as Homo habilis.
It ended around 11,000 years ago depending on the area. By this time the dominant species was Cro-Magnon.
Young Earth creationists believe that the Palaeolithic began around 6,000 years ago when stone tools began to be used by Adam and his descendants.