As land transport becomes electrified in the next few decades, that will free up fossil fuels for aircraft use, so we are looking a long time into the future. The technology exists now to reform using renewable or nuclear power any carbon compound into liquid hydrocarbons, the only obstacle is economics.
Carbon capture from the atmosphere, is new technology, air contains around 400ppm CO2, so 2500CuM of air has to be moved to move 1CuM CO2, the power needed to do that produces its own heat, used on a large scale might well be self defeating. It will certainly be massively costly, in fact it may well cost less to plant trees to achieve the same result.