We used the Spitzer Space Telescope's Infrared Spectrograph to create a high-resolution spectral map of the central region of the Cassiopeia A (Cas A) supernova remnant, allowing us to make a Doppler reconstruction of its threedimensional structure. The ejecta responsible for this emission have not yet encountered the remnant's reverse shock or the circumstellar medium, making it an ideal laboratory for exploring the dynamics of the supernova explosion itself. We observe that the O, Si, and S ejecta can form both sheet-like structures and filaments. Si and O, which come from different nucleosynthetic layers of the star, are observed to be coincident in velocity space in some regions, and separated by 500 km s −1 or more in others. Ejecta traveling toward us are, on average, ∼900 km s −1 slower than the material traveling away from us. We compare our observations to recent supernova explosion models and find that no single model can simultaneously reproduce all the observed features. However, models of different supernova explosions can collectively produce the observed geometries and structures of the interior emission. We use the results from the models to address the conditions during the supernova explosion, concentrating on asymmetries in the shock structure. We also predict that the back surface of Cas A will begin brightening in ∼30 years, and the front surface in ∼100 years.