Hydrogenation of CO₂ to methanol, ethanol and other oxygenates is an emerging attractive process in C₁ chemistry but remains a great challenge not least because of the intrinsic inertness of CO₂, difficulty in C–C bond coupling, and complexity in product distribution. Identifying the dominant reaction mechanism is therefore urgent but still lacking under real reaction conditions. In this work, by combining density functional theory calculations with microkinetic modeling, we predicted the activity plots of C₁ & C₂ oxygenates as a function of temperature and pressure on both stepped Pd(211) and flat Pd(111) surfaces according to the reaction network consisting of ∼150 elementary steps. We found that Pd(211) is more active than Pd(111), and the incremental effect is more remarkable for the production of C₂ oxygenates. An optimal reaction temperature of around 500 K is theoretically rationalized. COOH is the key intermediate in CO₂ activation, and the CO insertion with CH_x highly contributes to the C–C bond coupling. Formation of ethanol is directly competitive with that of methane. The activity dependences on reaction conditions are different between CO₂ and CO hydrogenation. The formation energy scaling relations of intermediates and transition states between the different Pd surfaces were established, providing a simplified strategy to estimate transition state energies on other surfaces for microkinetic simulation. All these constitute the key foundation for the rational design of metal catalysts and optimization of reaction conditions for CO₂ hydrogenation to C₁ & C₂ oxygenates.