Plot hole: In the opening scene, Wade applies to be an Avenger, and does it in the Sacred Timeline, the main MCU timeline, on Earth-616. Not his own, which the movie classifies in the next scene as Earth-10005. Assuming he can just do that (at the end of his second movie he certainly did stranger things than that with Cable's device), one fails to see the purpose of it. Let's assume he aced the interview and got hired; it's not his timeline. He does it to have a good relationship with his girlfriend. Who...is in a different universe. Whatever Wade does in the vastly different universe is not altering anything in his own. It was never going to work.
Suggested correction: He goes back to his universe. Think Thor...or the Guardians or Captain Marvel or whomever isn't Earth based. They "Assemble" then go back to protecting their little corner of the Marvel Universe.
Suggested correction: But it's Deadpool. When does anything he ever does make sense? He wanted to be an Avenger, he went out to be one, no matter what that meant in the literal sense. As long as he can say it, it's enough for him. Even if it is in a different universe/timeline, he can still say he's an Avenger. He is also a rule breaker, so maybe he can figure out how to make it work.
I knew this was going to be the objection to it; it's Deadpool, he can do whatever, etc. There are multiple times during the movie when he mentions things that he is not supposed to know because they are meant to be fourth-wall-breaking jokes. He references real-life actors, he interacted with them in previous movies. So they are absurdities with a purpose, and it's pointless to argue with comedy. But him being rejected by the Avengers is part of his motivations and of the 'serious' part of the plot, which is focused on his own universe and his girlfriend. Earth-616's Avengers though? The namedropping for nerds is an absurd choice when you think about it, which the movie does not want you to do, since it makes zero jokes about it. Without that caption it was not even going to raise any objection or paradox; he could have met with the Avengers of his universe, any universe - later in the movie Wolverine says "F*** the Avengers" as if he knows them.
Two things: 1. Even if he is able to join the Avengers on Earth-616, being part of a team might give him a sense of belonging and change his whole attitude. It wasn't to impress Vanessa about being an Avenger, it was to change his attitude which had soured after the events of the second movie. 2. It cleverly explains that the Marvel characters from the Fox universe were in their own universe and, to this point, have likely not been a part of the MCU.
Maybe his universe doesn't have Avengers and he found out about them through the MCU. That's what I'm saying. It's just a gimmick in the movie and actually doesn't affect the plot that much as he was given a task by the TVA (or whatever lone wolf from the TVA) and teams up with Wolverine. Him trying to be an Avenger and talking about it is just a running gag.
