Well, the water is pretty much literally right there to be picked up - cutting ice is a fairly well developed technology that shouldn't be heavily impacted by doing it in vacuum. And CO2 is even easier - it's everywhere, and existing vacuum pumps will have no problems collecting and concentrating it.
As for converting it to biomass - plants are extremely adept at converting water and CO2 into oxygen and biomass. And microbial ones like algae can reproduce exponentially over very short timescales, allowing you expand production just as fast as you can build greenhouses and collect the necessary trace elements.
You talk as though there's something magically more difficult about using mature technologies just because you're on another planet. Once you're inside an artificial pressurized habitat, the only immediate differences from being on Earth will be the strength of gravity, and the view out the windows.