Here is a mishmash of ideas...
A common way to open is to state your conclusion as concisely and directly as you can.
You don't always need exciting. Consider intriguing or surprising. Maybe controversial. What do you want the reader to feel right from the start? It isn't always excitement, but it's always some feeling. Curiosity. Outrage. Wonder. Humor.
What kind of essay is it? Informative? Raising awareness? Advice? Persuasion? Write an opening sentence that tells the reader what kind of amusement park ride they're climbing onto.
Surprise is often useful:
- A surprising observation.
- A surprising problem.
- A surprising conclusion.
- Surprising advice.
To maintain interest, you don't have to make the opening sentence of every paragraph punchy. What keeps me reading is that I want an answer to some question that the author has raised. How will the author solve the problem? Justify the conclusion? Make use of the surprising observation?
Maintaining interest can be as much about how you finish paragraphs as how you open them. Raise a new question in my mind. Then in opening words of the next paragraph, connect to that question. Maybe begin the answer. Maybe acknowledge the question and shift the focus to some other topic that will illuminate the (promised!) answer.