Lagomorphs (pikas, hares and rabbits) evolved it is theorised, in the Eocene Epoch, which was 55-35 million years ago.
There is in the fossil record a uniqueness from the early Eocene, so for me this stands to set it at 55 mya.
Apparently there used to be far more species; in the past (as in millions of years ago) over 230 species existed.
Other accounts put them at evolving 2 million years ago. (that's palaeontology for you)
Lagomorphs are not rodents.
There used to exist, in Minorca, a Lagomorph that weighed about 50 pounds, called Nuralagus rex.