I think I shared this somewhere else recently, but now that I'm awake:
Four teenagers are driving down the highway in a car, not really paying as much attention to the road as each other. The music's playing, they're joking around, whatever. Camera angle is moving back and forth, showing the kids' faces from different angles. There's a rumble, as if a jet has flown by too closely, and then you hear tires screeching and horns and crashing and as the kids turn to pay attention out the windshield, the camera angle spins to follow, and pans out through the windshield, focusing on two large feet in the middle of the road. The camera pans up and around the Sentinel, now showing us the view from the Sentinel's perspective. We see the outline of the car, and the thermal imaging signatures of the four passengers. Three are identified as human, one a mutant, and a lock is established as the Sentinel steps forward and leans down. We're back in the car as the roof is torn off, and the face of the Sentinel is RIGHT THERE. "Mutant apprehension in progress" the mechanical voice bellows.
Now, I don't care who you use for the young mutant, but for the sake of argument, let's go with Pixie. As the Sentinel reaches in, she shrugs off a coat, spreads he wings, and zips out of the Sentinel's grasp. Long shot as the Sentinel stands back up, outstretches an arm, and ordinance opens up, ready to fire. "Mutant attempting escape; target lock acquired" Suddenly, the Sentinel is struck in the face and rocked back, the missile flies wildly off course but again locks onto Pixie. We see Wolverine clawing the Sentinel's face apart as the rogue missile explodes behind Pixie, releasing a net hurtling towards her. Cyclops look back over his shoulder from the cockpit and yells "KURT!" Back to Pixie as Nightcrawler BAMFS in in midair, grabs her, and BAMFS out, letting the net fall harmlessly. A few feet away, they reappear and tumble to the ground, with Nightcrawler, tucking, rolling, and leaping to his feet in one swift move. "Do not fear, liebschien, my name is Kurt Wagner. Though in the Munich circus I was known as..." Scott yells with urgency "NIGHTCRAWLER!" "Ah, yes, I was just getting to that." He takes hold of Pixie and they BAMF out of sight as Logan is thrown to the ground right where they were crouched. He gets back up, torn to shreds, and begins to heal. He roars, ready to charge, but Cyclops intervenes over their communicators. "Logan! If you're done playing?" We see Iceman leap out of the Blackbird and ice-slide down to Wolverine, grabbing him along the way. They slide back up towards the Blackbird, but the Sentinel smashes the ice slide and they go flying. Jean, standing in the hatch, catches them in a telekinetic bubble while deflecting blasts from the Sentinel. "Oh, for... Auto-pilot, engage. Jean, civilians?" "All clear" And as we see Jean easing the two into the Blackbird, Scott emerges at the hatch. "Mutant targets..." An optic blast fills the better part of the screen, and levels the Sentinel. The hatch is closing, and we're at the interior of the Blackbird again, as Cyclops turns to the team. "Okay, does anyone have any idea WHAT the hell that was?" he asks (or something to that effect). Opening credits roll.
When you get back from the credits, we're en route back to Westchester. Nighcrawler and Meghan are seen in the back of the Blackbird, talking. She asks what that thing was. Jean comes back to explain that they were following a signal from Cerebro that led them to Meghan, and they happened across the robot attacking her. They don't know what it was, either. In the meantime, Cyclops is on an open channel to Xavier, furious that they were blindsided by this robot being there.
Eventually, you introduce Val Cooper as a government liason and reveal that the Sentinels have been produced covertly, yada yada yada. Throughout the movie, you seed some references to Apocalypse.
This movie takes place after X2 and has some references to the Phoenix, but she doesn't emerge until the next film, with Apocalypse attempting to harness it.