I'm a discovery writer; meaning I write without a plot, and see what happens. I don't have written character histories, or back stories, or a laundry list of traits or descriptions. If I need a physical trait, I invent it on the fly (and keep character notes so I stay consistent). I don't believe in being explicit about a theme, or grounding the story in some central moral dilemma, or any other "Meta" story or "higher purpose"; to me the job is entertainment and what is entertaining is a reader that wants to turn the page to find out what happens next. Their anticipation of the coming good or coming evil or coming action.
The truth is, ALL writers are in the "discovering the story" phase at some time or another, while they are inventing and outlining their plot, or if they just start writing from a blank page; it is just that the discovery writers (I object to the term pantser, it sounds pejorative: If they use pantser, I'll use plodder) believe the story feels more realistic has fewer problems if we let the characters become real people in our minds solving their problems intelligently, while plotters prefer to make their characters puppets doing what was planned for them.
To me, the latter too often feels unjustified and out of character, because it is: When the plotter finally gets around to dialogue and descriptions and feelings in their characters, actually starts writing the story the readers will see, this increasingly crystallizes the character and over the course of chapters they can grow (in my mind when I tried that approach) into a person that just would not do what the plot demands of them in Chapter 10, whatever act that is, it is no longer consistent with what she said and did in Chapters 3, 7, and 8.
In order to write a story this way, however, you need problems for your character. It is generally not enough to just have an image of somebody partially submerged in a bathtub. That image can help you define a character, or introduce her, but you need a reason for her to be there. Were I writing, this would not be a routine bath, but a bath that solves a problem for her; what was the problem this bath solves? Did she kill somebody? Is she masturbating? Is she crying? Is she tired and this is comforting? Is she hiding from her husband? Is she clothed and the house is on fire and she is about to wrap a wet towel around her head and run through the flames? Is this her way of recovering from a rape?
How did she come to be there? What happened before? Is this the opening scene, or is it whatever caused her to be there? Or should the opening scene be something in-between the cause and effect? (Probably so, if the cause is a lot of action; I don't want to open a story with extreme action, because readers typically won't care if they don't know who the characters are).
When I write, I generally have been thinking about a strong character with a BIG problem she is not sure how to solve. That problem will NOT appear at the opening of the story, but the end of ACT I (20% to 25% through). The beginning is composed of smaller problems, the first page is a "throwaway" problem she must deal with, a minor conflict of some sort that won't change her in any way, one of the many we all find in life. The car won't start. We wake up and the power is out. Or there is no hot water for the shower. The throwaway is not about the plot, it is about introducing our character being active and in conflict so we can see what she is like; not how she looks but what she does.
by in conflict I don't necessarily mean a fight or argument (although those are instances of conflict), I mean any situation in which the reader wants to know what happens next. So we give our girl X (no power AND no hot water AND she has to get ready for work), so the reader wants to know "what does she do about it?", or "what happens next?"
That is why people read, to find out what happens next! When they lose interest in that, they put down the story.
As an author, my job is to devise such conflicts, one after another (and hopefully one leading to another), and let my characters decide, based on who they are as they develop in my mind, what they must do next. Their story grows that way, through cause and effect. Each decision they make puts them in a new situation that should have another problem, another reason for the reader to wonder "what happens next?" in a chain reaction to the final resolution of the major dilemma at the end of Act I.
Typically, a "formula" for a discovery writer is to open with the status quo world of the main character, one they are used to, and also open with a minor, everyday problem in that world, something that will pull the reader (by wondering 'what happens next') through the character building and world building that must be done in order to ground your story in some imaginary time, place and culture. This problem can be an excuse for the character to do something minor and out of the ordinary: Her car won't start, she is going to be late to work, so she calls an Uber to bring her to work (or some made-up competitor of Uber). Or she had to skip breakfast, so she stops on the way to work at a pastry shop.
That out of the ordinary act can snowball. She can meet new people, for example. It does not have to snowball, this problem can just go away: She called the Uber, got to work on time, and will have to call another to get home. Or a coworker offers her a ride, and that does lead to something.
But the ordinary problem has done its job if it lets you introduce your character and world. You can introduce a completely different problem after that, one that can lead or snowball into your big-ass conflict that will drive the story. Whether that is her falling in love or trying to find and kill somebody is up to you.
Before I start putting words on paper, I have in my mind my character, her big problem, and her sidekick. About the time I have written ACT I, I will have some quarter page to half page description of an ending that will work, but it is provisional and subject to change. If my characters develop in a way that makes this ending not work, I must come up with another ending. I don't really worry about how to get there, this is always the problem they want to solve so I let them choose how to get there and what to do.
Stephen King is also a discovery writer, and one of the top 5 best selling authors of all time. I'd suggest you read Stephen King's book, "On Writing". It is how a best selling discovery writer approaches the profession, without plotting. This technique works, and anybody that says they just can't plot, can still write great fiction.
Edit to clarify, in response to Galastel's comment about "needing to know where I am going..."
The biggest problem plotters have is the middle; not so discovery writers; their biggest problem is endings, wrapping things up.
I always keep some ending in mind that will work, and if I feel I must write something that makes my ending no longer work, I must also find a better ending I can make work. So I never write myself into a corner, never take a lesser ending, and if I don't know the exact path to get where I am going, I at least know the place and a compass direction to get there.
For me, my ending typically changes two or three times in the course of writing the story; usually the final change seems to be around 50% of the way through the story. For that reason, I don't try to come up with a killer ending before I begin writing, my first ending can be clichéd. I don't write unsuccessful endings (I write endings that eliminate the main threat but may be costly to my MC or leave her with much to DO after the ending, but I leave no doubt the story-driving problem is over). So I won't begin writing unless I can think of some half-ass solution to the story-driving problem. I'll likely improve on it later.
Also, for knowing where I am going, I subscribe to the rough percentages in the Three Act Structure, where turning points are, reveals are, etc. So the first 10% of the story is intro; at 15% we should see a turn into the main conflict area; by 20% it should be clear, etc. These were derived from successful stories, and I consider them a structure descriptive of successful stories. Take note the stories in question existed before the authors knew of the Three Act structure; it just turns out that these are the proportions people happen to like in their stories. So I don't have to plan these milestones, but I know if I am telling the story right, they should appear, or I should be leading into one. In that sense, I know where I am and where I should be going; and I know if I am running too long in a part or need another scene, etc.
I don't necessarily know how LONG my story is, but I can judge from the intro: If that is 10%, then an equal amount is what is needed to end Act I with a big problem. After the fact, I can edit to bring my story closer to the Three Act structure; but I don't adhere to it down to the page, just roughly within 5% or so.