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Using public data from the NEWFIRM Medium-Band Survey (NMBS) and the Cosmic Assembly Near-Infrared Deep Extragalactic Legacy Survey (CANDELS), we investigate the population of massive galaxies at z > 3. The main aim of this work is to identify the potential progenitors of z ∼ 2 compact, massive, quiescent galaxies (CMQGs), furthering our understanding of the onset and evolution of massive galaxies. Our work is enabled by high-resolution images from CANDELS data and accurate photometric redshifts, stellar masses, and star formation rates (SFRs) from 37-band NMBS photometry. The total number of massive galaxies at z > 3 is consistent with the number of massive, quiescent galaxies (MQGs) at z ∼ 2, implying that the SFRs for all of these galaxies must be much lower by z ∼ 2. We discover four CMQGs at z > 3, pushing back the time for which such galaxies have been observed. However, the volume density for these galaxies is significantly less than that of galaxies at z < 2 with similar masses, SFRs, and sizes, implying that additional CMQGs must be created in the intervening ∼1 Gyr between z = 3 and z = 2. We find five star-forming galaxies at z ∼ 3 that are compact (Re < 1.4 kpc) and have stellar mass M∗ > 1010.6M; these galaxies are likely to become members of the massive, quiescent, compact galaxy population at z ∼ 2. We evolve the stellar masses and SFRs of each individual z > 3 galaxy adopting five different star formation histories (SFHs) and studying the resulting population of massive galaxies at z = 2.3. We find that declining or truncated SFHs are necessary to match the observed number density of MQGs at z ∼ 2, whereas a constant delayed-exponential SFH would result in a number density significantly smaller than observed. All of our assumed SFHs imply number densities of CMQGs at z ∼ 2 that are consistent with the observed number density. Better agreement with the observed number density of CMQGs at z ∼ 2 is obtained if merging is included in the analysis and better still if star formation quenching is assumed to shortly follow the merging event, as implied by recent models of the formation of MQGs.