I've written openings for textbook chapters, lectures, essays and a memoir, and the thing I've become surest of is that a first sentence is a promise about what kind of attention the piece will require. Readers can tell within a line whether they're about to be explained to, entertained, or asked to think. They decide about you before they've decided about your subject.
Most first drafts start a paragraph too early. Mine do. I write my way in, clearing my throat about why the topic matters, and the actual beginning turns out to be sitting there in paragraph two, already doing the work. The fix is unglamorous. Delete the first paragraph and read what's left. About seven times out of ten it starts better.
The reason is that the throat-clearing paragraph is written for me, not for the reader. It's the part where I convince myself I'm allowed to write the piece. Once that's done, the paragraph has served its purpose and can go.
A good opening does one of a small number of things. It puts you inside a specific moment. It states a position plainly enough that you want to argue. It tells you something true you hadn't quite noticed. What it shouldn't do is announce itself. "In today's fast-changing landscape" is a sentence that promises nothing except more sentences like it.
I'm suspicious of the very clever opening for a related reason. A line that's too pleased with itself sets a standard the rest of the piece has to keep meeting, and usually can't. Then the whole essay reads as a slow decline from its own first line. Better to open at the level you can sustain.
When I'm teaching this I ask for the second sentence. That's where you find out whether the first one was real. A first sentence can be borrowed, remembered, or lifted from something you half-read. The second one has to belong to it. If a student can't write a second sentence that follows from the first, the first was decoration.
There's a version of this test I use on my own drafts. I read the opening and ask what it obliges me to do. If the answer is nothing in particular, it isn't an opening, it's a warm-up. A real first sentence narrows the field. It rules things out. After it, there are essays you can no longer write, and that constraint is the useful part.
The other thing I've learned is to stop protecting openings. I used to spend a morning on a first line before writing anything else, which is a good way to spend a morning and a bad way to write a piece. Now I write something serviceable, finish the draft, and come back. By then I know what the essay actually turned out to be about, which is rarely what I intended, and the right opening is usually a sentence already sitting in the middle somewhere. I move it to the front and cut what came before it.
That happens often enough that I've stopped being surprised. The piece tells you where it starts. It just doesn't do it until you've written far enough in to hear it.