TRUTH OR CONSEQUENCES, N.M.—British billionaire Richard Branson on Sunday soared more than 50 miles above the New Mexico desert aboard his Virgin Galactic rocket plane and safely returned in the vehicle’s first fully crewed test flight to space, a symbolic milestone for a venture he started 17 years ago. Branson, one of six Virgin Galactic Holding Inc employees strapped in for the ride, has touted the mission as a precursor to a new era of space tourism, with the company he founded in 2004 poised to begin commercial operations next year. The success of the flight also gave the entrepreneur bragging rights in a highly publicized rivalry with fellow billionaire Jeff Bezos, the Amazon online retail mogul who had hoped to fly into space first aboard his own space company’s rocket. Sunday’s launch of the VSS Unity passenger rocket plane marked the company’s 22nd test flight of its SpaceShipTwo system, …