The class was for screen adaptation, but the advice applies to any story. =) I improved the beginning of a story by working on the characters' journeys and goals.
Another screenwriting teacher did not believe in writer's block. She suggested to check if you strayed from the story's path at one point. Perhaps you put in a scene for its own purpose instead of the whole story's purpose. Sometimes you have to let go moments or lines. Save the draft though because you could try using that scene in another story.
Screenwriter Nicholas Meyer wanted to express his dislike of punk rock music through the time-traveling hero in Time After Time. Meyer had to omit the scene, but he rewrote it in Star Trek IV: The Voyage Home. I found the well-known scene, but the song was changed: