A Dyson sphere is a tough ask at our stage of technology. But you can build habitats in free space - yes. Start with Stanford Torus or O Neil cylinder.
This Stanford Torus of 10,000 people could be built using materials from a tiny Near Earth Asteroid two or three hundred meters across, or the original proposal, send a small buldozer to the Moon, do a not that large excavation on the lunar surface and send the materials into space with rail guns.
You could build it close to Earth easy to get to, easy to trade with Earth.
Can argue one way or another about whether it's easier to build habitats in space or on a surface - but certainly to make something as spacious as this - and with spinning for full gravity - needs to be done in space, doesn't seem too practical to make something as big as this and also rotating for artificial gravity on the Moon or Mars.
As you say - once we've got safe interplanetary flight we are pretty much most of the way there.
The one thing we do need is radiation shielding. It is a problem long term - we could survive maybe a year or two without - but that means taking on a significant risk of developing cancer which would reduce your life span - who wants to do that? As for young children and living there full time, then we do need radiation shielding.
So that's the main thing that limits construction, the mass of the shielding.
And as for available materials, there's enough material in the asteroid belt to build radiation shielding for a thousand times the land surface area of the Earth. That's a calculation that goes back to the 1970s. So, yes you are right, and that's the reason that the Stanford group, and O'Neil etc designed their habitats in free space, not on the Moon or Mars. Plus accessibility to Earth - build them close to Earth and they can make solar panels and do mining and trade with Earth.
As for Dyson Sphere though - that's much harder. Where do you get the materials? What do you do about radiation shielding? Why do it anyway? That's for a future perhaps because you need so much power for your civilization that you need to capture all the solar power from the sun. That could be a motivation for Dyson sphere or swarm - and you maybe don't live on the surface particularly - just use it to collect power. So then it could be a thin flimsy thing just opaque and able to collect solar power.
However there's an underlying question to ask here - is it good to colonize the solar system - and then the galaxy?
We haven't done such a great job with the Earth - but at least limited to this one planet and incentive to sort things out because we are stuck here - and in many ways are also doing that.
But - in the galaxy as a whole - what would we do to the galaxy if you let humanity loose on it? With exponential growth then we could spread to the entire galaxy within just a few million years even at slow sub light speeds.
With the almost unlimited future technology? Able to build self replicating machines, able to manipulate genes and create new creatures not descended from anything now alive, able to create mixtures of life and machine, able to do nanotechnology?
The self replicating machines and newly created creatures seem in some ways most tricky. Because - if let out of control they could do almost anything to the galaxy. Whatever the machines were programmed to do. Just because someone made a mistake and set one of them loose on the galaxy.
Maybe there's an answer to that, I hope there is - but - best I can think myself is - that we need in some way to limit the way we explore the galaxy - e.g. to explore it rather than to colonize, some restriction on the colonization. Because - I find it hard to suppose that a galaxy with every star inhabited by humans would be a peaceful place and a good place to live in, if we are anything like we are today - and even if it was - is harder to ensure against stupidity - if some of them accidentally let loose self replicating machines, which then improve themselves and take over the galaxy - then - how do you make sure that won't happen?
Remember this is happening over a canvas of millions of years with civilizations rising and falling, and humans maybe losing intelligence, regressing in places, still with all the technology and power, maybe obedient robots to do whatever they ask, but with the intelligence and moral responsibility say of a four year old - could let a wave of von Neumann machines on the galaxy just through stupidity or not understanding what it is they are doing (like the sorcerer's apprentice) - how do you ensure against something like that?
And what about other ETs in the galaxy- who might be vulnerable to the future us, just as we worry we might be vulnerable to present ETs? If it's bad for them it's bad for us to behave like that.
I've got no answer, except to suggest that we take things slowly, no need to have colonization and expanding to fill the galaxy as our aims. But instead to be aware there could be issues in doing that - and to focus on exploration and understanding - as best we can anyway as our immediate goals.
To recognize as clearly as possible that, really, we understand so very little yet, with all our science. And to proceed with the aim to explore and find out more before we start making major changes to our galaxy. When understanding does dawn and we can see our way ahead it may then be clear what to do.
That could help delay things - and maybe we'll find a solution ourselves - or else - find answers from other ETs who have encountered the same issues and found a way through them - maybe even ETs in other galaxies.