How to write a compelling opening paragraph?

I would perhaps start with a story, a personal example. Ex: "A girl stands in doorway of her living room, face brilliant red from tears. She's covered in mud and bleeding from one hand. Her mother looks at her and says hello, but somehow misses the condition the girl is in because the mother isn't truly seeing her." That also shows how you can take a personal experience and take the word "I" out of it. If you want to get technical, you'd take the story out of first person and put it into third person. Hope this helps a little bit, even with the random weirdness that was my example. :)