Can a home be built to try and keep radon out?
Yes. This is called radon resistant construction. Usually about four inches of gravel is put down below the basement or foundation, with plastic sheeting put over this. The radon gas will pass through the gravel, but most of it won’t get through the plastic.
Then, you seal and caulk all openings in the concrete foundation floor, and put in a gas-tight vent pipe that runs from under the foundation through the house to the roof. So, most of the system to reduce radon, if you need to do that later, is already there. Building a home with these radon resistant measures costs less than half as much as putting them in after the home is already built.