When people think of radiation protection, they think of the magnetosphere. But they really need to be thinking of the atmosphere. There's a reason traveling on a plane gets you a higher dose of radiation and it's not a weaker magnetosphere.
Perhaps a thick shell of water suffices. In the order of meters, perhaps one to four meters. Perhaps combine it with lead, in the order of centimeters, perhaps ten centimeters, then one meter of water would suffice.
Numerous long-duration spacecraft designs incorporate water storage in the outer structure, or a high-radiation shelter within a water storage structure, for just this purpose.
Water attenuates radiation quite rapidly. And has other uses.
There will never, ever be such atmosphere on Moon as its on Earth. Too low gravity for example, solar winds would scrub it pretty fast even if you would somehow create it 100% with a snap of fingers.
Its nice dreaming about options but this aint realistic.
We are only talking about "fast" relative to normal planetary timescales.
My understanding is that it would still take hundreds of years for the solar wind to strip away the atmosphere. If a civilisation had the technology to quickly put an atmosphere on the moon, it has the technology to continually replenish the atmosphere as long as that civilisation lasts.
It would never be practical (or a good idea) but a post-scarcity society could pull it off as a vanity project.
