Direct capture of CO2 from ambient air is technically feasible today, with commercial units already in operation. A demonstrated technology for achieving direct air capture (DAC) is chemical separation of CO2 in a steam-assisted temperature-vacuum swing adsorption (S-TVSA) process. However, the potential to develop scalable solutions remains high, requiring a detailed understanding of the impact of both process design and operation on the performance of the DAC unit. Here, we address this knowledge gap by presenting a state-of-the-art process simulation tool for the purification of CO2 from ambient air by a 5-step S-TVSA process. By considering the benchmark adsorbent APDES-NFC, we conduct multi-objective productivity/energy usage optimization of the DAC unit, subject to the requirement of producing a high purity CO2 product (>= 95%). For the base case scenario, we find a maximum productivity of Pr-max = 6.20 kg/m(3)/day and a minimum specific equivalent work of W-EQ,W-min = 1.66 MJ/kg. While in reasonable agreement with published data, our results indicate that the description of both competitive adsorption and adsorption kinetics are key factors in introducing uncertainty in process model predictions. We also demonstrate that the application of formal optimization techniques, rather than design heuristics, is central to reliably assess the process performance limits. We identity that system designs employing moderate CO2 sorption kinetics and contactors with low length-to-radius ratios yield the best performance in terms of system productivity. Finally, we find that moderate-high ambient relative humidities (50-75%) offer significantly favourable performance, and that a wide range of feed temperatures (5-30 degree celsius) can be accommodated via process optimization without a significant impact on performance.