I considered lava tubes, but on the Moon they have their own problems.
Earth is a destructive place, so if nature or man creates it, and it remains over time, it is sound, which includes mines, natural caves and lava tubes. But the Moon is not like that. If it creates something that is not sound, it remains. So you cannot trust the ceiling, walls or floors of a lava tube until you have gone over them with test equipment.
The next problem is that whatever tunnels you have are limited in size by your ability to pressurize and heat them. And it would be far preferable if they were horizontal instead of sloping and irregular. The first tunnel may be only 50’ in length by 7’ in circumference, except for the flat floor.
A man made tunnel can be started in the floor of a crater, going into the side of the crater, in a place chosen as a relatively temperate place, likely near the pole where ice can be mined. A lava tube is wherever.
The next problem is that whatever tunnels you have are limited in size by your ability to pressurize and heat them. And it would be far preferable if they were horizontal <><>instead of sloping and irregular
We have the off-the-shelf technology, experience, and engineering smarts to overcome all of the obstacles you present.
Utilizing the moon's natural geological features to establish an initial beachhead on the moon, is far more doable (and far less expensive) than mounting a robotic mission of heavy tunnel boring equipment.
Carving out our own tunnels and underground chambers is obviously the preferred permanent habitat solution, but those missions will have to come later, as we build up our manned presence and infrastructure.
Think in gradients. Establishing permanent, robust, lunar bases, is a gigantic endeavor which will take many years to fully put in place. It has to be done in baby steps, one bit at a time, similar to how we established human outposts in Antarctica.