one upside is many modern rockets use methane, synthesizing methane with pv/wind power would be much lower impact, depending on how much of the exhaust is actually at escape velocity it could be very slightly carbon negative, like new forged steel with ore prepped with clean hydrogen.
Correct me if I'm wrong but I am under the impression that Starship does not use that, the least expensive fuels for rockets are highly CO2 emitting, and the least expensive fuels are what will get rolled out in mass numbers if SpaceX, Blue Origin, and others succeed in building a rocket transportation industry.
Starship, Blue Origin's upcoming heavy-lift rocket New Glenn, and United Launch Alliance's upcoming heavy-lift rocket Vulcan, are all powered by methane and oxygen.
starship uses methalox, a combination of methane and oxygen. I'm far from an expert, but my understanding is the methane comes from refining LNG.
That's generally where methane comes from today, but in time it may come from captured CO₂, e.g. see https://terraformindustries.com/ (disclaimer: I am a minor investor).