I don’t know about methane as an aromatic/hybridized ring building block. Anything is possible with chemical synthesis but is it energy feasible.
There’s always plant hydrocarbon feed stocks but I think using arable land to make plastics is dumb and also carbon intensive. (I do wear cotton clothing tho because you need to make trade offs).
https://www.siemens-energy.com/global/en/home/press-releases...
It's not a solved problem, though. Truly renewable carbon feedstocks have to source their carbon from the air, not the soil, which has to be continually measured. Land selection for carbon feedstock projects has to ensure it doesn't induce land-use change in other locations due to displacing other things like food production, etc. Otherwise the emissions and environmental harm from those downstream effects have to be included in the carbon positive/negative calculations for the project.
All this can be extended by addition of hydrogen. Naively, if you process a carbohydrate into hydrocarbons, about half the carbon is lost as CO2. Adding hydrogen allows the oxygen to be carried off as water rather than CO2 (or, the CO2 to be converted to hydrocarbons and water in a second step.) Hydrogen currently comes from natural gas but that will have to change anyway, with the hydrogen being produced by (for example) electrolysis of water.