The advanced molybdenum-based rare process experiment (AMoRE) aims to search for neutrinoless double beta decay () of Mo with  of Mo-enriched molybdenum embedded in cryogenic detectors with a dual heat and light readout. At the current, pilot stage of the AMoRE project we employ six calcium molybdate crystals with a total mass of 1.9 kg, produced from Ca-depleted calcium and Mo-enriched molybdenum (). The simultaneous detection of heat (phonon) and scintillation (photon) signals is realized with high resolution metallic magnetic calorimeter sensors that operate at milli-Kelvin temperatures. This stage of the project is carried out in the Yangyang underground laboratory at a depth of 700 m. We report first results from the AMoRE-Pilot  search with a 111 kg day live exposure of  crystals. No evidence for  decay of Mo is found, and a upper limit is set for the half-life of  of Mo of  at 90% C.L. This limit corresponds to an effective Majorana neutrino mass limit in the range .