This study develops a multiperiod mixed-integer linear programming model for strategic planning of direct air capture (DAC) supply chains across Europe aiming at minimizing overall costs under uncertainty. DAC is pivotal for achieving net-zero targets and removing CO2 from the atmosphere to enable negative emissions. The optimization considers uncertainty in key parameters to ensure resilient decision-making. The model incorporates the influence of ambient air conditions on DAC performance, with temperature and humidity impacting productivity and energy consumption. Country-specific energy costs and greenhouse gas emission factors are accounted for, impacting the net cost of CO2 removal. Results indicate that with ambitious targets, technology learning curves, and renewable electricity transition, costs can fall to approximately 121 <euro>/t CO2 by 2050, with 108 <euro>/t attributed to capture costs. The findings highlight the importance of technological advancements and provide a systematic framework for policymakers to design resilient and cost-effective supply chains for large-scale deployment, positioning DAC as a potential decarbonization alternative for hard-to-abate emissions.