Direct air capture (DAC) in combination with storage of CO2 can lower atmospheric CO2 concentrations. This study investigates the environmental impact of a new fast-swing solid sorbent DAC system, including CO2 transport and storage, over its life cycle, using prospective life cycle assessment. This DAC technology is currently on technology readiness level 5 and is expected to operate on an industrial scale by 2030. The technology was upscaled to the industrial scale and future changes in the background over the lifetime of the system were included, such as electricity grid mix decarbonization. Environmental trade-offs for the new DAC system were assessed by comparing environmental benefits from CO2 sequestration with environmental burdens from production, operation and decommissioning. We considered three electricity generation configurations: grid-connected, wind-connected, and a hybrid configuration. We found net environmental benefits for all configurations and background scenarios for ecosystem damage and climate change. Net human health benefits were observed when the electricity grid decarbonizes quickly and without the use of a battery. The environmental benefits increase with decreasing electricity footprint and are comparable with other DAC technologies. This illustrates that the new DAC system can help to meet the climate goals.