DELAFIELD, Wis.—Fifteen miles south of Erin Hills, where the U.S. Open begins on Thursday, Bob Lang sits in an office surrounded by mementos from the golf course he built. There are early design drawings, the original clubhouse cornerstone, a framed photo on one wall and, on a recent morning, two enlarged landscape photos spread across the wooden floor.

They are remnants of one the most improbable tales in golf history: How a little-known Wisconsin businessman with only a passing interest in the sport turned a rural cow...