I'll through this one out there as a contender for the earliest story from a sci-fi writer using precognition.
Young Strickland's Career, was written by J D Beresford and published in his short story collection Signs and Wonders in 1921.
The rather bleak story covers the story of a middle aged man that witness a vision in a crystal ball, concerning the future of his then young son aged 7 or so. The narrator tells of the incident when Strickland sees the vision.
And when the vision came, neither he nor I related it in any way to his ancient search....
He came to my rooms one evening after dinner, produced the crystal from his pocket, and tossed it over to me.
“A present for a sceptic,” he said. “I’ve finished with it.”
I might have thought that he was clearing up the lumber of his old fancies if it had not been for his manner; but the garment of his initiation still clung to him and affected me with the strangeness of its mystery.
“What did you see?” I asked.
“Oh! don’t say you believe in it,” he said; “after all your jeers at me.”
“Did you see anything?” I insisted, nursing the crystal in the cave of my two hands. I stared into it and saw the faint pink of my magnified palm. No vision came to me; yet I was aware of some potency in the thing.
“Perhaps some reflection, some translation of one’s sub-consciousness....” I ventured.
Strickland sneered. “By God, I hope not,” he said.
“What were you—looking for?” I asked.
“For nothing. I wasn’t looking for anything,” he said. “I picked the thing up by the merest accident. I was going to give it to the little girl—as a plaything.”
“And then....” I prompted him.
“I saw a picture in it. It snatched my attention. I wasn’t thinking....”
“And the picture?”
“Hell. Just hell. The real thing; none of your picturesque flames and torture. It came out at me, as it were, and it was—well, the abomination of desolation, nothing more nor less than that.”
“But....” I began.
He interrupted me. His eyes were fixed on the vision of a future that had become a fragment of his past. “A waste,” he said, in a low, thoughtful voice. “A dead, horrible waste ... all black and pitted and furrowed ... it looked as if there had been some awful, blasting eruption ... or as if the whole earth had been scorched and blighted by some unimaginably vast fire. But, oh! the terrible gauntness and death of it all.”
He paused and threw his head back with a queer laugh before he continued in a new tone, “It was just a silly nightmare, that’s all. And it had its inevitable element of the grotesque. In the middle of that waste there was a scarecrow, a live scarecrow—digging. Digging turnips, if you please. Oh! it was bosh, of course, absolute bosh. I shall have forgotten all about it next week. But I couldn’t give the crystal to the little girl after that. You can keep it. Tell me if you get anything....”
So I kept the crystal, and sometimes stared into it. But no vision came to me.
The story continues jumping forward in time to the year 1919. Strickland requests that the narrator accompany him to France to help search for his son you is listed as missing after the events of the First World War.
The denouement is below....
I do not believe that he remembered his vision when, after a week’s fruitless enquiry, we came one afternoon to the historic desert that had once been beautiful France. Certainly, he made no reference to his old experience; but he was almost senile. I noticed a difference in him, even in that one week.
But I remembered; and I had a fit of cold shivering that I could not control when we came out on to the awful plain that they now call The Plain of the Dead, and saw the figure of that one demented peasant, dressed in the grotesque relics of two nations’ uniforms.
He was digging feverishly with his pointed spade, and I heard the ring of it as it struck.
It was not a turnip that he wrenched up.
The thing rolled towards us....
Young Strickland’s head had always been a queer shape.
The collection is available on Project Gutenberg website where these quotes have been collated from.