The England striker scored from the penalty spot and tapped home from close-range as the Premier League giants ran riot at the Pasadena Rose Bowl in the Dutchman's first game.
New recruits Ander Herrera and Luke Shaw were handed starts, while Van Gaal - David Moyes' replacement - opted for a 3-4-1-2 formation that was similar to that used by the Netherlands at the World Cup in Brazil.
The change in system proved effective during the early exchanges and Welbeck got the ball rolling in the 13th minute, benefiting from an advantage following a foul on Juan Mata before striking the ball off the post and into the net from a full 25 yards.
United gained a stranglehold of proceedings in the 42nd minute, when Rooney converted a spot kick after the referee awarded a penalty for handball against the Galaxy, who are fourth in the Western Conference standings in MLS.
Rooney then put the result beyond doubt on the stroke of halftime, pouncing on some awful defending to bundle the ball over the line for his second of the match.
Van Gaal made wholesale changes at the break, with Darren Fletcher and Herrera the only two players to keep their places in the XI, and it ultimately disrupted the flow of the game.
However, Young cut the ball back in the box and it found its way to James, who scored a similar goal to Welbeck just past the hour mark, before the 20-year-old struck again with five minutes remaining.
But United were not done there with Young getting in on the action with two goals in as many minutes during the closing stages to add some sheen to the scoreline.