Some people could for sure. But these houses would be much more expensive to build than any house on Earth. Because you have to build them to hold in the atmosphere at many tons per square meter - that's why they may be shaped like a dome, it's the strongest shape for containing pressure.  Dome or very strong cylinders probably with rounded ends.

Like this, the ESA's plan for a Moon Village

Should we build a village on the Moon?

As you see in the artist's impressions - they  also have to be covered with a few meters of regolith to keep out the solar storms (would be well beyond the influence of Earth's magnetic field which protects the ISS) - or to have storm shelters - but if you are living there long term you'd want the whole of the interior to be protected.

You would need full pressure spacesuits to go out of doors. Any outside repairs need to be done in spacesuits - or using remote controlled telepresence robots.

The habitat itself will probably have a limited lifetime before it has to be replaced by a new one. Which you have to ship from Earth.

They may be able to recycle their CO2 to make oxygen however by then, and grow their own food. If not you have to ship many tons from Earth every few months just to feed the astronauts.

So anyway - yes it's well possible that we have a few dozen, even a few hundred people on the Moon by then. I see it as a bit like a research station in Antarctica

Princess Elisabeth Antarctica

It's an outpost, a place where scientists live while studying Antarctica, and tourists can visit sometimes also. May have tourist hotels on the Moon who knows.

But not a place where you'd set up home if you just want somewhere to live. The Moon and anywhere in space is far far more inhospitable than Antarctica. Mars is also. There are many places on Earth where we have research outposts and where adventurers visit, and also places that only see humans for a few weeks of each year - e.g. tops of mountains in the Himalayas - and many deserts - and like the sea bed. We don't colonize everywhere on Earth either. And I don't think myself that we are going to colonize space in the near future. It could happen in the distant future if we start to have settlements of tens of thousands of people in a big dome in space, city sized dome or underground caverns, because then you might get economies of scale. Maybe if you have a big dome large enough to hold ten thousand people, as the area to volume ratio gets less, as the dome gets larger, it might be easier to maintain per person. Maybe eventually when it gets large enough, the cost is spread out enough so that it doesn't cost too much per person and gets affordable as a place to live.

But I don't see that any time soon. And just as well. Because think what it would be like if we had extremist terrorists in space with space technology, able not just to fly airplanes at buildings, but spacecraft with velocities of kilometers per second? And bearing in mind that space habitats are far more fragile than any Earth building.

I think we need to make sure that however we explore and settle space, and maybe colonize it a bit, that we do it in a peaceful way. We don't want a future with battling space colonists living in deep underground bunkers to protect themselves from kilometers per second impacts.

For sure the first few hundred, even first few thousand, would be people with high ideals probably, and peaceful people also hopefully. But when you get to the first few million, if that is possible at all?

Perhaps it can be done safely. We have adopted various other technologies widely in our world that would lead to disaster if you were to transfer them back into the C 19, say.

But if so, to do that I think it's best not to rush it, not to have a big push to send lots of people into space right now. I think it's the pace of change that would be the main risk and if we do it slowly we should find a way, hopefully.

And there is nothing to say we have to colonize space. As we don't colonize the sea bed, or Antarctica or deserts or mountain tops, it's not like every place we could colonize, we have to colonize.

As for the argument that we have to go into space to escape destruction on Earth - well - it could easily be the opposite, that going into space if it means millions of people out there with high technology, including dictators, terrorists etc, it could be one of the things that leads to disaster for us in the future.

And there is nowhere in space as habitable for humans as Earth, and no disaster that could make Earth as uninhabitable as anywhere in space as to do that, you'd have to strip away all its atmosphere, and oceans. Nothing we can do would do that, and it's hard to beat the advantage of having a breathable air and being able to do light weight construction of houses that don' t have to hold in tons per square meter of pressure, and being able to walk out of doors without wearing a spacesuit :).

And yes resources in space may well be very useful on Earth. Or we may build thin film mirrors in space to concentrate sunlight and convert that to electrical power.

But that doesn't require us to colonize space with millions of settlers either. If we go into space to find resources to help the Earth, well at most maybe thousands or perhaps tens of thousands, but we won't need millions of space miners to do that.

A lot of it may well be done robotically, which is far safer for humans than doing it in spacesuits which can be damaged. There isn't any huge rush to send humans into space in large numbers.

Let's just go slowly one step at a time as we do when exploring Antarctica - a similar destination though space is far more difficult a place for humans to live than Antarctica.

See also my Why we can't backup Earth on Mars, the Moon or anywhere else in our solar system