If so, the hard part is getting the carbon capture cheap enough, not the hydrogen.
I crunched the numbers and you need around 13.6 kilograms of carbon and 4.54 kilograms of hydrogen to make enough natural gas to give you 1GJ of heat when combusted (this is how natural gas is priced in the metric world - 1 GJ is roughly 0.95 MMBTU).
If you're extracting CO2 from the air, roughly 27% of the CO2 is carbon, the rest is oxygen.
Doing the maths suggests that at current ballpark prices for CO2 direct air capture of $1000/tonne, the cost of capturing enough CO2 to make a GJ of natural gas is about $50. That's before you've done the processing to convert your CO2 and hydrogen into natural gas and oxygen.
So let's assume an order of magnitude improvement in air capture costs. Even at $100 per tonne, the CO2 capture cost is around $5. When you combine that with the approximately $4.50 worth of hydrogen required, that gives an input cost of around $9.50. That's way more than domestic natural gas currently costs in the US, but it's in the ballpark that you could subsidise your way around that at scale, and the numbers look pretty reasonable compared to imported LNG in Europe and Asia.
So to me this suggests that, if your business plan is to make methane, the hydrogen part is almost a sideshow to getting direct air capture costs down.