Looked up the speed of US air to air missiles. They range from Mach 2.5 to 4.0. Seems like maneuverable speed for a jet is sub Mach. So escaping it would be hard indeed.
I haven't seen the latest Top Gun, so can't speak to the film... But the original was chock full of aviation nonsense... Though still fun!
In addition to what others have shared, I'll add...
Dodging missiles is definitely hard, but also doable under many circumstances. High speed is necessary for overtaking, but detrimental to maneuverability.
For a given g-load factor (I. E. Bank angle in a level turn) the radius of turn increases with the square of the aircraft's true airspeed. Thus, a high sub-sonic jet in a ~9g turn likely has a much tighter turning radius than a Mach 2+ missile, even though the missile may also be capable of a much higher g-loading.
Also, not all missiles approach from the rear of the aircraft, some even approaching head-on. This is over simplified, but overtaking an aircraft to either the left or right, then paralleling their course and approaching laterally from the side requires less maneuvering from the missile while simultaneously making escape for the aircraft much harder. It's almost like vehicle "A" (the missile) overtaking vehicle "B" on the highway, and once beside vehicle "B", vehicle "A" merges into vehicle "B's" lane and runs them off the road.
Interestingly, the scene in the movie The Incredibles where the business jet is shot down is rather on point (in an over the top cartoon sort of way). Fun fact, this is also how bats often approach insects while feeding in-flight.