It is technically possible to make sustainable fuels without biomass by sucking carbon out of the air, with the caveat that it requires lots of electricity to run the process. This is known as “power-to-liquid” fuel and there are several small-scale demonstration projects in the works, although it’s probably not something that would be remotely economically viable anytime soon.

Power-to-Liquid Fuel for Sustainable Aviation — Sustainable Review
The aviation industry has seen growth in innovation to power the next generation of aircraft. Power to Liquid Fuel is one the solutions that has seen rapid development.
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One big drawback is that even if the process is run on 100% clean & renewable electric power, that same power would be better put to use in replacing coal power plants, reducing the carbon footprint for cement production, or similar dirty earth-bound processes for the forseeable future. But if we do eventually have a surplus of clean electric power someday then it would be a good option, so I’m glad they’re researching it. Seems more achievable than large electric passenger jets that are battery powered with the same speed and range capabilities of existing jets