In the case of 'Dracula', the early paragraphs create an atmosphere of mystery and dread. There are mentions of strange happenings in Transylvania. This immediately gives us an idea that the plot will involve some sort of dark, supernatural events. The first paragraphs might introduce characters in a certain way. In Dracula, Jonathan Harker is introduced as someone who is about to enter an unknown and dangerous situation, which hints at the overall plot of his encounters with the vampire.
Well, for example, in 'The Adventures of Tom Sawyer', the first paragraphs show Tom getting in trouble for his mischievous behavior. From this, we can predict that the story will likely be about his various adventures and escapades as he gets into and out of trouble. The first paragraphs often set the tone, like here it's a bit of a naughty and adventurous tone.
Take 'Oliver Twist' for instance. The first paragraphs describe Oliver's birth in a workhouse and his early, difficult life. From this start, we can anticipate that the plot will revolve around Oliver's struggle for a better life, his encounters with different people in the harsh society of that time, and his search for identity and a place where he belongs. The first paragraphs give us a sense of the social context and the character's starting point, which are important clues for predicting the overall plot.