Framing out concrete lower garage

A homeowner in a cold climate (winter design temps down to -22°F) is planning to finish a below-grade garage space, about 676 square feet, that's concrete on three sides with a framed wall on the fourth. The plan is storage in back and a woodshop up front, with a mini-split heat pump (a compact heating and cooling unit) added later on the exterior wall side. The problem: the space stays damp and musty, even with a commercial dehumidifier running, and wet spots have shown up on the floor near where it meets the wall, suggesting moisture is getting in from outside the concrete.

The homeowner's plan is to frame over the concrete with 2x4s and plywood, using taped rigid foam board (XPS) against the concrete first, plus thin rubber flooring on top. The open question is whether that foam-and-framing approach is enough, or whether the ongoing moisture problem needs to be solved first before finishing the walls.

For anyone with a similar below-grade or garage space, the takeaway is that framing and insulating over damp concrete without first tracking down and fixing the water source can trap moisture behind the new wall, where it's hidden and harder to deal with. Wet spots at a floor-wall joint usually point to water or vapor moving through the concrete from outside, not just interior humidity a dehumidifier can fully handle.