The teenage full-back joined the Red Devils from Southampton and is relishing making his home debut after fighting back to full fitness in the USA
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The 19-year-old has since missed out on a place in the starting XI, with a resurgent Ashley Young preferred at left wing-back, and faces a battle to be selected for United's Premier League opener against Swansea City on August 16.
The former Southampton starlet should be given a chance to impress at some stage against Valencia on Tuesday, though, and is relishing playing at the Theatre of Dreams following a manic tour of the USA.
"It’s been a crazy few weeks," Shaw told reporters.
"I got back from the World Cup and came up here to get everything sorted with the medical.
"I’d heard a lot of things about how crazy it was on tour and I witnessed that.
"Until you have gone out to America, you don’t know what it’s like.
"That surprised me, but I have heard it’s even worse in Asia. It was really nice to see how many supporters United have got out there.
"As a kid, it’s a dream to play at Old Trafford and it’s one of the biggest arenas in the world.
"To know it’s going to be my home ground is something special. I can’t wait to get my first touch on the pitch, just to relish it."
The match against the Liga outfit represents Van Gaal's final opportunity to see his side on the pitch ahead of the new campaign, and as thus reportedly sent a scout to watch Nuno's team during their Emirates Cup campaign.
And Shaw admits that he has been impressed with the thoroughness of his manager as they look to build on their International Champions Cup win and chase further honours.
"Every game is serious. We want to improve as a team and the way we can do that is going into the game properly by using the scouts to discover what they are like and see how we are going to play against them.
"The main thing is obviously the first Premier League game against Swansea, the first match of the season, but we want to keep improving as a team and getting used to the formation so we will be flying when the season starts.
"You have got to be positive and, for me personally, I have come here to win trophies.
"That is something everyone wants, not just me. Everyone in that dressing room is looking to do that.
"We all can’t wait to get started."