There are many great ways to start a short story

Typically, essays are written in the voice of the author, whereas short stories are written in the voice of a narrator, a persona created by the author to tell the story. As you are writing about a short story and are referring to what the storyteller says, you should not refer to what the "author" says but to what the narrator says.

But not every type of opening is right for every story

There are many great ways to start a short story. But not every type of opening is right for every story. Here are seven types of short story opening, and how to decide which one is right for you.

that almost makes the story feel like a personal essay.

Writing Short Stories & Essay Writing

The skills needed to narrate a story well are not entirely the same as the skills needed to write a good essay. Some wonderful short fiction writers are not particularly good essayists and vice versa. Still, it is useful to look at those elements that make up a good narrative and know how to apply what we learn toward making our essays as dramatic as possible whenever that is appropriate.

How to Start a Story - Graeme Shimmin: alternate …

This is possibly the most common type of short story opening. The action doesn't really begin in the opening paragraph, instead we join the characters in a pause before the action, and this allows us to get to know the characters and the setting first. This can be a workmanlike "Smith yawned and looked around his space capsule" thing. Or it can be a gorgeous literary flourish, that sets the mood and creates a strong image in the reader's mind at the start of the story. Often, the action begins in the second or third paragraph.
Why you might use this one: If the setting is a huge part of your story, or if a big part of your goal is to establish a powerful mood. Or if your story isn't really about plot, but about a particular feeling.
Why you might not: Sometimes you want your story to get going a bit faster. Sometimes the ideas, or the plot, are more important than the setting. And sometimes you find that you can do scene-setting in the second or third paragraph, and it'll have more impact.
"Jarvis stretched himself as luxuriously as he could in the cramped general quarter of the Ares. 'Air you can breathe!' he exulted. 'It feels as thick as soup after the thin stuff out there!'" — Stanley G. Weinbaum, "A Martian Odyssey"
"Bianca Nazario stands at the end of the world. The firmament above is as blue as the summer skies of her childhood, mirrored in the waters of la caldera; but where the skies she remembers were bounded by mountains, here on Sky there is no horizon, only a line of white cloud." — David Moles, "Finisterra"
"The swell was gently lifting and lowering the boat. My breathing grew slower, falling into step with the creaking of the hull, until I could no longer tell the difference between the faint rhythmic motion of the cabin and the sensation of filling and emptying my lungs." — Greg Egan, "Oceanic"
"The balloon of a Phoenix-class airship is better than any view from its cabin windows; half a mile of silk pulled taut across three hundred metal ribs and a hundred gleaming spines is a beautiful thing." — Genevieve Valentine, "The Zeppelin Conductors' Society Annual Gentlemen's Ball"

Short Stories Short works of fiction

This is sort of similar to the previous one, except that instead of the third person narrator explaining, it's the first-person narrator saying something reflective, that almost makes the story feel like a personal essay. The first-person narrator muses about some ideas, or about his/her feelings. When it's done right, this opening can create a more intimate feeling, as well as putting us right into your main character's brain — rather than just showing us the outside world through your character's eyes, the way a typical first-person opening does. This can also be the start of a rant, or an extended monologue, by the first-person narrator.
Why you might use this one: If you're writing in the first person anyway, why not have the first-person narrator soliloquize a bit? This can pack quite an emotional punch, or help the reader to bond with your narrator right off the bat. Plus it blurs the line between fiction and essay, which is always a plus.
Why you might not: Sometimes we bond more with your first person narrator if he/she gives us some scene-setting or tells us something about what he/she was doing at the start of the story, instead. That way, we're not just getting to know your character, we're getting to know him/her in the world. Plus it really depends how philosophical you want to get.
"There is a principle in nature I don't think anyone has pointed out before. Each hour, a myriad of trillions of little live things — bacteria, microbes, "animalcules" — are born and die, not counting for much except in the bulk of their existence and the accumulation of their tiny effects. They do not perceive deeply. They do not suffer much. A hundred billion, dying, would not begin to have the same importance as a single human death." — Greg Bear, "Blood Music."
"You sent us out here. We do this for you: spin your webs and build your magic gateways, thread the needle's eye at sixty thousand kilometers a second. We never stop, never even dare to slow down, lest the light of your coming turn us to plasma. All so you can step from star to star without dirtying your feet in these endless, empty wastes between. Is it really to much to ask, that you might talk to us now and then?" — Peter Watts, "The Island"
"I remember the future. The future was glorious once. It was filled with sleek silver spaceships, lunar colonies, and galactic empires. The horizon seemed within reach; we could almost grasp the stars if we would but try." — Michael A. Burstein, "I Remember the Future"
"You ask me if I can forgive myself? I can forgive myself for many things." — Neil Gaiman, "The Truth is a Cave in the Black Mountains..."
"I wanted to be washed up on a foreign shore, but this can't be it. I wanted, first, for a long, long beach, so I could lie there and recover for a while. After all, I'd be tired." — Carol Emshwiller, "All washed Up While Looking for a Better World."