Good starter paragraphs can engage readers by creating mystery. For instance, if you start with something like 'She found a strange object in the attic. It was small, shiny, and seemed to hum with an unknown energy.' This makes the reader want to know what the object is and what will happen next.
They can also engage readers by introducing an interesting character. Like 'The detective with the crooked smile and a past he couldn't forget walked into the crime - scene. His eyes scanned the room, looking for clues that no one else could see.' The character's description and the situation he is in are intriguing and make the reader want to follow his story. Additionally, good starter paragraphs can set a mood. A paragraph that says 'The rain poured down relentlessly, drenching the city streets. The streetlights cast a dim, yellowish glow on the wet pavement. People hurried by, heads down, as if they were all running from something.' This creates a moody atmosphere that draws the reader in and makes them curious about what's going on in this dreary setting.