While we have no primate fossil material prior to the Eocene Epoch, the first primates are thought to have evolved prior to the Paleocene Epoch (66–56 mya), possibly as far back as 90 mya, during the ...While we have no primate fossil material prior to the Eocene Epoch, the first primates are thought to have evolved prior to the Paleocene Epoch (66–56 mya), possibly as far back as 90 mya, during the Late Cretaceous Period. With the extinction of the dinosaurs at the end of the Cretaceous, many terrestrial niches became available and predation pressures were somewhat relaxed.