In researching this answer to a different question, I came across an earlier example of a bootstrap paradox in the 1904 story The Panchronicon by Harold Steele MacKaye, available on project Gutenberg here. In this story the characters travel back from 1898 to Shakespeare's time, and in Chapter XII, "How Shakespeare Wrote His Plays", a time traveler named Phœbe, who is very familiar with his plays, offers to help him complete Hamlet's famous soliloquy in return for some help getting a message to one of her companions:
"Ay, there, and in more than this!" Phœbe exclaimed. "You have spoken of Hamlet, Master Shakespeare. Guy hath told me something of that tragedy. This Prince of Denmark is a most unhappy wight, if I mistake not. Doth he not once turn to thought of self-murder?"
"Ay, mistress. I have given Sir Guy my thoughts on the theme of Hamlet, and have told him I planned a speech wherein should be made patent Hamlet's desperate weariness of life, sickened by brooding on his mother's infamy."
"'To be or not to be, that is the question,'" quoted Phœbe. "Runs it not so?"
"This passes!" cried Shakespeare, once more all amazement. "I told not this to your friend!"
"Nor did I from Guy receive it," said Phœbe. "Tell me, Master Shakespeare, have you yet brought that speech to its term?"
"No," he replied, "nor have I found the task an easy one. Much have I written, but 'tis all too slight. Can you complete these lines, think you?"
"My life upon it!" she cried, eagerly.
He shook his head, smiling incredulously.
"You scarce know what you promise," he said. "Can one so young—a damsel, too—sound to its bitter deeps the soul of Hamlet!"
"Think you so?" Phœbe replied, her eyes sparkling. "Then what say you to a bargain, Master Shakespeare? You know where Sir Guy Fenton may be found?"
"Ay, right well! 'Tis a matter of one hour's ride."
"So I thought," she said. "Hear, then, mine offer. I must perforce convey a message straight that touches the life and honor of Sir Guy. To send my servant were over-dangerous, for there may be watchers on my going and coming. Will you go, sir, without delay, if that I speak for you the missing lines completing young Hamlet's soliloquy?"
Shakespeare looked into her face for a few moments in silence.
"Why, truly," he said at last, "I have here present business with my fellow-player Burbidge." He paused, and then, yielding to the pleading in her eyes: "Yet call it a bargain, mistress," he said. "Speak me the lines I lack and straightway will I take your word to Sir Guy."
"Now blessings on thee!" cried Phœbe. "Give me straight the line you last have written."
At once the poet began:
"When he himself might his quietus make——"
"With a bare bodkin"—broke in the excited girl. "Who would fardels bear, to grunt and sweat beneath a weary life, but that the thought of something after death—the undiscovered country from whose bourne no traveller returns—puzzles the will, and makes us rather bear the ills we have than fly to others that we know not of. Thus conscience does make cowards of us all, and so the native hue of resolution is sicklied o'er with the pale cast of thought, and enterprises of great pith and moment by this regard their currents turn awry and lose the name of action."
"No more—no more!" cried Shakespeare, in an ecstasy. "More than completely hast thou made thy bargain good, damsel unmatchable! What! Can it be! Why here have we the very impress of young Hamlet's soul—'To grunt and sweat beneath a weary life'—feel you not there compunction and disgust, seeing in life no cleanly burden, but a 'fardel' truly, borne on the greasy shoulders of filthy slaves!"
He turned and paced back and forth upon the gravel, repeating without mistake and with gestures and accents inimitable the lines which Phœbe had dictated. She watched him, listening attentively, conscious that what she saw and heard, though given in a moment, were to be carried with her forever; convinced as well that she was for something in this, and thankful while half afraid.
On its own, I suppose it might be possible to interpret this episode in terms of a changeable timeline, like a scenario where there was an original version of history where Shakespeare finished the soliloquy himself, and Phœbe only changed things by giving him his own words from a different timeline. However, there are other elements of the story that point to a fixed self-consistent timeline rather than a changeable timeline. In real-life history, a woman named Delia Bacon put forth the the theory that the works of Shakespeare were actually written by Francis Bacon, and Phœbe references this theory at the beginning of the story, before she has done any time-traveling:
"Look, Rebecca!" cried Phœbe, as she entered the door, "here's a new book Mrs. Bolton lent me to-day. All about Bacon writing Shakespeare's plays, an' how Bacon was a son of Queen Elizabeth. Do you s'pose he really did?"
During the course of the story the time travelers meet Francis Bacon, and in the final chapter he ends up accompanying them when they travel back to their own time, with the result that he himself turns out to be the originator of the Shakespeare theory, with "Delia Bacon" being his pseudonym. After that he is eager to return to his own time, having already learned of the "brilliant future" he will have after returning. So, all this suggests a fixed-history model where the effects of the trip through time were already part of the time travelers' history before they actually made the trip.
The date-recording instrument must have been deranged in some way, for when, after a great number of eastward turns around the pole, it marked the year 1898, they had really only reached 1857. Supposing themselves to have actually reached the year erroneously indicated by the recorder, they set off southward and made a first landing in Hartford, Connecticut.
Here they discovered their mistake, and returned to the pole to complete their journey in time. All but Francis Bacon. He declared that so much whirling made him giddy, and remained in Connecticut. Alas! Had Phœbe known the result of this desertion, she would never have consented to it.
Bacon, who had read much of Shakespeare while in the Panchronicon, found on returning thus accidentally to modern America, that this playwright was esteemed the first and greatest of poets and dramatists by the modern world. Then and there he planned a conspiracy to rob the greatest character in literary history of his just fame; and, under the pseudonym of "Delia Bacon," advanced those theories of his own concealed authorship which have ever since deluded the uncritical and disgusted all lovers of common-sense and of justice.
Copernicus Droop, on returning his three remaining passengers to their proper dates and addresses, discovered that his sole remaining phonograph, with certain valuable records of Elizabethan origin, had disappeared. As he owed a grudge to Francis Bacon, that worthy fell at once under suspicion, and accordingly Droop promptly returned to 1857, sought out the deserter, and charged him with having stolen these instruments.
It was not until the accused man had indignantly denied all knowledge of Droop's property that the crestfallen Yankee recollected that he had left the apparatus in question in the deserted mansion of Newington, where he had stored it for greater safety after Bacon's first unexpected visit.
Without hesitation, he determined to return to 1598 and reclaim his own. Bacon, who had learned from modern historical works of the brilliant future in store for himself in England, begged Droop to take him back; and as an atonement for his unjust accusation, Droop consented.
It is not generally known that, contrary to common report, Francis Bacon was not arrested for debt in 1598; but that, during the time he was supposed to have been in prison, he was actually engaged in building up in his own behalf the greatest hoax in history.