You need to get the Dome Fossil inside Mount Moon. The fossil can't be missed, you have to pick it up in order to continue on the blocked path. You are only allowed one fossil, so choose carefully! The other one, the Helix fossil, will give you an Omanyte.
Much later in the game when you reach Cinnabar Island, a scientist in a lab will revive the fossil for you, and the Old Amber fossil you found in Pewter City's Museum.