As Joss Whedon said when Age of Ultron was released, Marvel works hard to try to make these very expensive crossover movies work for as large an audience as possible:
Kevin Feige and I are fanboys, straight up. But we also know that if you just spend your time catering to the fans you make something that is hermetically sealed. The first question we always ask is: ‘What is the way in for someone who has never seen a superhero movie?’ You need to be thinking about everybody all the time.
This is borne out by the box office takings. Infinity War made $2,048 million; Ant-Man and the Wasp made $622 million. While it's possible the exact same audience saw Ant-Man once and Infinity War three or four times, Marvel can't reliably assume that even a majority of the Endgame audience has seen anything other than Infinity War.
So in short, don't worry. You and your girlfriend can understand and enjoy Endgame on its own terms as a direct Infinity War sequel (obviously make sure she sees that), without worrying that you're missing something. Feel free to take it on its own terms, and if any of the characters resonate with you, go and check out their standalone or crossover movies at your leisure.
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With that said, the emotional effects of some events on the characters will be clearer and more impactful if you’ve seen what they’ve been through and cared about in previous movies. The MCU is unique in Hollywood movie history, in that the oldest characters have narrative threads running across multiple solo and team-up movies all the way back to 2008.
Hopefully without spoiling you too much for Infinity War or Endgame, these eleven/twelve movies cover the major beats for the oldest characters, and don't miss out any crucial plot elements:
- Captain America: The First Avenger introduces the two defining relationships of Cap’s life, and lays the groundwork for a minor-but-cool “Oh, it’s that guy!” in Infinity War.
- The Avengers shows the birth of the team, gives sufficient introduction to Loki & Thor and their relationship, does enough to explain who Tony and Bruce are without seeing their individual movies, and in the mid-credits sequence introduces our erstwhile Infinity War antagonist.
- Thor: The Dark World shows how Loki & Thor’s relationship develops after The Avengers, which will be important for Ragnarok — and the mid-credit sequence mentions Infinity Stones for the first time.
- Guardians of the Galaxy covers Gamora and Nebula's history; establishes that like Thor, the Noble Rabbit doesn't know what raccoons are; explains what the deal is with Infinity Stones; and gives us another peek at Thanos.
- Captain America: The Winter Soldier introduces Falcon, explains why SHIELD is less of a presence in Age of Ultron, and develops Cap’s enduring bromance with a certain seasonal warrior.
- Avengers: Age of Ultron introduces Vision and Wanda, establishes Tony’s state of mind (he even says Endgame in it!), develops Nat and Banner's relationship, and teases Mr Purple mid-credits again.
- Captain America: Civil War gives you Tony's fraught family background, puts all of the earth-bound pieces in place for Infinity War, introduces two major new characters (and introduces Ant-Man enough to skip his movie), while basically being the best superhero movie ever made. Make sure to watch the mid-credits sequence to see where T'Challa comes from.
- Guardians of the Galaxy Vol. 2 introduces Mantis, shows Nebula’s development, and develops Quill & Gamora's relationship — all of which are pretty crucial in Infinity War.
- Doctor Strange makes the Sorcerer Supreme's role in defending the earth (or rather its dimension) clearer, which will be relevant in Endgame.
- Thor: Ragnarok shows you Thor, Loki and Banner & Hulk's journey in the run-up to Infinity War; and in the mid-credits scene, leads right into it.
- Avengers: Infinity War — actually, skip this. Nothing much happens.
- Optional: Captain Marvel explains the Infinity War post-credits scene, fully introduces Carol, and in its mid-credits scene bridges the gap to Endgame. This is skippable if you're pressed for time, but it's slightly surprising how little exposition Endgame contains for Carol's role and powers.
If, on the other hand, twelve movies isn’t enough, add one or both of these:
Iron Man 2, at the start. It's not as enjoyable a movie as Iron Man, but it introduces Rhodey, Fury, Widow, Howard Stark, and Tony's self-destructive streak.
Ant-Man and the Wasp, right before Endgame. It's good fun, and tees up Ant-Man's role in the finale (although that is sufficiently explained in Endgame itself).
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(And once you've seen Endgame, if you want to go back and experience the whole Infinity Saga from the start, I have a great alternative viewing order for you.)