Introduction:
We can give the moon an atmosphere, how do I know this? Because Titan which is about the same size as our moon has a thick atmosphere. The difference is that Titan is cold, damn cold! So if we dig a 290km tunnel we can create a solar shielded section inside the moon that can sustain atmosphere and expand that section horizontally. The scale altitude I have worked out is 12.4km.
Main Article:
Similar to my idea to dig in Mars I figured this would be more practical and useful for the moon. If we dig 290km deep: we can sustain an atmosphere of 1 bar. This was calculated by working out the scale altitude of the moon being 12.4km.
The illustrated vertical section will be cryogenic temperature gas. This makes mining the moon from the inside out more practical and safe with an atmosphere eliminating the risk of decompression. I had to work out the scale altitude of the moon despite it being a vacuum. It still has gravity. The main difference between our moon and Titan is that Titan is colder, this is why Titan can have an atmosphere while our hot moon cannot. So I figured we might as well replicate Titan in the moon with a tunnel that the sun cannot heat up. This way we can seal the tunnel into sections. The vertical section of the tunnel in the moon can be air sealed but not to keep in or out any pressure but instead to keep the warm air in (cold air out). The hatch only needs to be thermally shielded. It does not need to be rated to keep a vacuum in our out. If the hatch breaks we have time to to repair/replace the hatch without the risk of violent de-compresion. We will only be fighting the cold. So we can suit up in suits that are less demanding that just keep us warm while we repair it. We can also have multiple doors seals as redundancy. Let me know in the comment section if you like this idea or not!