The relative lack of investment in the squad, and a couple of key injuries, mean that the Dutchman faces fewer selection dilemmas than he may have wanted. However, some difficult decisions will still have to be made.
Here are the areas in which Van Gaal will have to chose wisely...
Daniel Taylor of the Guardian suggests United may only have "two fully fit senior defenders" going into the Swansea game.
With Luke Shaw ruled out, and Jonny Evans and Antonio Valencia doubtful, Van Gaal will have to improvise.
Tyler Blackett seems most likely to deputise for Jonny Evans. The new boss will have to chose between him and Michael Keane, assuming he does not want to deplete United's already stretched midfield resources by using Darren Fletcher as part of his back three.
With Rafael da Silva injured and Valencia "undergoing treatment," according to Taylor, United's right-wing-back will most likely be Ashley Young. This will mean Reece James being deployed on the left.
A back five of Young, James, Blackett, Phil Jones and Chris Smalling has a very thrown-together look about it. Van Gaal and his coaches will have plenty of organisational work to do.
Choosing Ander Herrera's partner in the centre of midfield is Van Gaal's only dilemma here.
The three realistic contenders are Darren Fletcher, Tom Cleverley and Marouane Fellaini. Fellaini did not join up with the full squad until their return from their pre-season tour, so he may be a couple of weeks behind in terms of cohesion and fitness.
He did, however, impress in his brief cameo at the end of United's friendly against Valencia on Tuesday night. It was not just his winning goal, but his tidy use of the ball and resilience in the face of unpleasant ironic cheers from the crowd, which whipped up every time he was in possession.
Assuming Fellaini's lack of time with Van Gaal's first-team squad counts against him, the decision is between Cleverley and Fletcher.
Of the two, Fletcher had the more impressive pre-season and is presumably first-choice. Fans will be hoping more difficult dilemmas lie ahead in this area of the pitch.
Before Welbeck's injury against Real Madrid, Van Gaal started all of United's friendlies with a front three of Mata, Rooney and Welbeck.
Welbeck's presence offers a number of things. His willing running and excellent tracking back offers both Rooney and Mata the freedom to be less disciplined about their positioning. He also allows Rooney to be the true No. 9 in the partnership.
When Javier Hernandez was used, Rooney was naturally forced into a more support-oriented role, and United looked less fluent as a consequence.
A third option could be to use Mata, Rooney and United's new No. 11, Adnan Januzaj. Januzaj has been on the same pre-season schedule as Fellaini, which may count against him. If he is available for selection then his pace, passing and composure in front of goal could make him a fine foil for Rooney.
Shinji Kagawa could perhaps be considered for either Mata's place or a place alongside Herrera in midfield, but it would be a surprise. A second-half substitute appearance would be less of an eyebrow-raiser.
Nani also played as a second striker on United's tour, but he was largely ineffectual.
It remains clear that Van Gaal only really has top-quality alternatives in forward areas. These will only improve when Robin van Persie returns to action.
The rest of the squad is self-evidently too thin. The relative lack of difficulty in guessing United's best XI highlights that decisive action is still required if United are going to compete for the title. United should have enough firepower to be too much for Swansea City, but greater challenges lie ahead.
Just over two weeks remain of the transfer window to bring in the reinforcements that would allow Van Gaal's men to face them better prepared.