Spoilers for Avengers: Infinity War follow. Major spoilers!
According to Marvel Studios president Kevin Feige, Spider-Man: Far From Home will start minutes after Avengers: Endgame, meaning it's definitely a sequel to the upcoming film. Of course, going into the massive ensemble, Peter Parker is dead, snapped from existence before Avengers: Infinity War came to an end. He is also listed as a missing person in the first Endgame trailer, but he's casually swinging around New York City in front of the old Avengers tower in his new solo film trailer.
The only explanation here is that Spider-Man is coming back to life, and it will be in a brand-new timeline created when Avengers: Endgame travels backward in time, to end at a point in time prior to where it began.
Some possible clues came when the Spider-Man: Far From Home trailer dropped. The first look at the joint venture between Marvel Studios and Sony Pictures intentionally removed the years from Peter Parker's passport. Viewers get July dates but no year beside them, a crucial element to any valid passport -- and that's not an accident; it's because telling the audience which summer in which Far From Home takes place would reveal whether it's before or after Peter turned to dust in Infinity War (which isn't tremendously important, considering that is never going to happen in this timeline).
Meanwhile, in the Avengers: Endgame trailer, Scott Lang is seen showing up at the Avengers facility in "archive" footage. This means it is old footage, despite Ant-Man never having been to the Avengers in the present timeline other than when he showed up, fought Falcon, stole something, and left. A moment later, when Captain America asks if this is an old message, Natasha only tells him, "That's the front door," but she does not tell him when it's the front door.
The last time the Marvel Cinematic Universe saw Scott Lang, he was headed into the Quantum Realm in Ant-Man and The Wasp's post-credits scene where he was warned not to get sucked into a time vortex. While the capabilities of time vortexes remain unknown, it's a bit of a coincidence that Scott is popping up in the apparently in the past, and likely ready to play a key role in taking on Thanos.
With Endgame picking up a few days after Infinity War's ending as revealed by Tony Stark in his hopeless space drift, it's possible the Avengers reunite, travel back in time, stop Thanos before he gets started, and therefore create a brand-new timeline where Spider-Man never dies.
This new timeline would line up with a world after Spider-Man: Homecoming, because Aunt May knows Peter is Spider-Man in Far From Home. It's a piece of information she learned at the end of their first movie and is on display early in Far From Home's trailer. Far From Home would then take place before Avengers: Infinity War began -- somewhere in that sweet spot between Homecoming and Infinity War -- in a world where Infinity War is never going to happen.
In conclusion: Spider-Man: Far From Home can start "minutes after" Avengers: Endgame, is a prequel (of sorts) to Avengers: Infinity War, and still progresses the Marvel Cinematic Universe forward in a brand-new timeline ,making it a prequel and sequel and a brand-new story all at once.
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