Another approach they could take is starting with a fully formed team but telling the story from Kitty Pryde's POV. I can already picture the first 15 minutes.
Kitty Pryde is your everyday American teenage girl living in Chicago. She goes to school and lives a normal life... until news outlets, television, and the internet begin spreading stories of the "mutant menace". Her world starts to fall apart as social tension rises around her, affecting her school climate, her home life, and everything around her. At this point she barely knows what a "mutant" is.
One day, she begins to develop strangely severe migranes at odd intervals. (at home, school, dance class with Stevie Hunter, etc)
A few days later, a strange man in a wheelchair shows up to her house and introduces himself as Professor Charles Xavier . Xavier invites her to join Charles Xavier's school for the gifted. Thinking that things will blow over in due time, Kitty assures herself that the migranes are nothing and the school she's already at will serve her well enough. She declines Xavier's invitation.
Over time the migranes get worse and worse, until she collapses and falls through a solid wall. Kitty begins to seriously wonder if she might really be a mutant like Xavier said. She visits the coffee-a-go-go to have a drink and collect her thoughts.
Walking home, a gang of suspicious characters (Friends of Humanity) follow her, having seen her phase through the wall earlier.
"We saw what you did back there, MUTIE!" they shout as they attack Kitty Pryde. As Kitty frantically runs for her life, she is unable to control her powers. Backed into a corner, she desperately begs for SOMEONE to save her. At the last moment, a lightning bolt strikes one of the attackers, and a crimson beam blasts another across the street. Another attacker steps on a glowing playing card that promptly explodes. Kitty desperately runs to make a break for it as clouds of black smoke can be seen on the edge of the screen and in the background. Another man grabs her and is promptly punched by a metal fist (we don't see who the fist belongs to). Kitty slips and hits her head.
The last thing she sees as her consciousness fades are a couple of blurry figures of a large man and a woman in green punching the bad guys. The screen fades to black as she hears a voice with a southern drawl say...
"G'night sugah."
Kitty wakes up in a white room, unsure of where she is. She hears a voice speaking to her (as a nod to the OG X-men movie in 2000). Unsure of who she's speaking to, she runs out of the room and is introduced to Professor X. He explains where she is (the mansion), and that she is a mutant with the X-gene. Professor X continues as he tells Kitty that he teaches mutants about their powers. At that moment, he introduces his students and a door begins to open.
"To me, my X-men."
The door opens.
...and there's nothing there.
Kitty is puzzled, wondering where everybody is.
"I thought you said your students were going to--"
The X-men come busting through the wall right behind Kitty and Xavier as the logo shows up onscreen for the first time. (Note: You could also add Rogue and Gambit to the screenshot above.)
. Wolverine is only stopped when Cyclops steps up to lead the team in battle, and professor X finally gets thru to wolverine's mind and relaxes him as hulk pummels him. Then he shares his old millitary nickname of Wolverine. And "they chose me because I'm the best at what I do. And what I do...is KILL
"
