The promising direct dimethyl ether (DME) production through CO2 hydrogenation was systematically analyzed in this research by synthesizing, characterizing, and testing several catalytic structures. In doing so, various combinations of precipitation and impregnation of copper- and zinc-oxides (CuO–ZnO) over a ZSM-5 zeolite structure were applied to synthesize the hybrid catalysts capable of hydrogenating carbon dioxide to methanol and dehydrating it to DME. The resulting catalytic structures, including the co-precipitated, sequentially precipitated, and sequentially impregnated CuO–ZnO/ZSM-5 catalysts, were prepared in the form of particle and electrospun fibers with distinguished chemical and structural features. They were then characterized using XRD, BET, XPS, ICP, TGA, SEM, and FIB-SEM/EDS analyses. Their catalytic performances were also tested and analyzed in light of their observed characteristics. It was observed that it is crucial to establish relatively small-size and well-distributed zeolite crystals across a hybrid catalytic structure to secure a distinguished DME selectivity and yield. This approach, along with other observed behaviors and the involved phenomena like catalyst particles and fibers, clusters of catalyst particles, or the whole catalytic bed, were analyzed and explained. In particular, the desired characteristics of a CuO–ZnO/ZSM-5 hybrid catalyst, synthesized in a single-pot processing of the precursors of all involved catalytically active elements, were found to be promising in guiding the future efforts in tailoring an efficient catalyst for this system.