A slab poured at ground level has many of the same openings as a basement floor, and a crawlspace is directly connected to the soil. Indoor air pressure is usually a little lower than the soil's, so the house draws radon in through whatever openings it has.
Foundation type changes how radon is fixed, not whether a home can have it. Slab homes are usually treated with soil suction under the slab, and crawlspace homes with a sealed plastic sheet and a fan drawing from under it.
What to do next: test a regularly used room on the ground floor with a short-term kit, and follow up if the result is high.

