We present initial results from a James Webb Space Telescope (JWST) survey of the youngest Galactic core-collapse supernova remnant, Cassiopeia A (Cas A), made up of NIRCam and MIRI imaging mosaics that map emission from the main shell, interior, and surrounding circumstellar/interstellar material (CSM/ISM). We also present four exploratory positions of MIRI Medium Resolution Spectrograph integral field unit spectroscopy that sample ejecta, CSM, and associated dust from representative shocked and unshocked regions. Surprising discoveries include (1) a weblike network of unshocked ejecta filaments resolved to ∼0.01 pc scales exhibiting an overall morphology consistent with turbulent mixing of cool, low-entropy matter from the progenitor’s oxygen layer with hot, high-entropy matter heated by neutrino interactions and radioactivity; (2) a thick sheet of dust-dominated emission from shocked CSM seen in projection toward the remnant’s interior pockmarked with small (∼1″) round holes formed by ≲0.″1 knots of high-velocity ejecta that have pierced through the CSM and driven expanding tangential shocks; and (3) dozens of light echoes with angular sizes between ∼0.″1 and 1′ reflecting previously unseen fine-scale structure in the ISM. NIRCam observations place new upper limits on infrared emission (≲20 nJy at 3 μm) from the neutron star in Cas A’s center and tightly constrain scenarios involving a possible fallback disk. These JWST survey data and initial findings help address unresolved questions about massive star explosions that have broad implications for the formation and evolution of stellar populations, the metal and dust enrichment of galaxies, and the origin of compact remnant objects.