The dramatic first images with James Webb Space Telescope (JWST) demonstrated its power to provide unprecedented spatial detail for galaxies in the high-redshift universe. Here, we leverage the resolution and depth of the JWST Cosmic Evolution Early Release Science Survey (CEERS) data in the Extended Groth Strip (EGS) to perform pixel-level morphological classifications of galaxies in JWST F150W imaging using the Morpheus deep learning framework for astronomical image analysis. By cross-referencing with existing photometric redshift catalogs from the Hubble Space Telescope (HST) CANDELS survey, we show that JWST images indicate the emergence of disk morphologies before z~2 and with candidates appearing as early as z~5. By modeling the light profile of each object and accounting for the JWST point-spread function, we find the high-redshift disk candidates have exponential surface brightness profiles with an average Sersic (1968) index n=1.04 and >90% displaying "disky" profiles (n<2). Comparing with prior Morpheus classifications in CANDELS we find that a plurality of JWST disk galaxy candidates were previously classified as compact based on the shallower HST imagery, indicating that the improved optical quality and depth of the JWST helps to reveal disk morphologies that were hiding in the noise. We discuss the implications of these early disk candidates on theories for cosmological disk galaxy formation.