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Once upon a time — well, no, not really. The flow(s) of time in this story don't correspond to the timeline in our universe.
Suppose there are two universes, which we can call X and Y. Each of these universes is much the same as our own, in many respects: physics behave largely the same way, and each universe has three dimensions of space, and one dimension of time. Matter is acted upon by force, and cause leads to effect. One interesting feature of universes X and Y, though, which is unknown thus far in our own universe, is the possibility of time travel. At least in theory.
In universes X and Y, matter and information can be transmitted back in time, so long as that transmission is self-consistent and doesn't cause a paradox. In fact, it's impossible to send anything back through time that would lead to circumstances that didn't already happen: each universe has only one timeline, so there's no possibility of creating offshoots. Nor can the effects of time travel "overwrite" a previous history. From our privileged position as outside observers, we can see each universe as a four-dimensional object, where all time-travel events have already happened, or are already happening, or will already happen, depending on where we choose to focus our attention. There is no room for an "original timeline" to be overwritten.
One might think this would have all sorts of interesting ramifications for society. And it would, if there were any societies in universes X and Y. As a matter of fact, both universes are quite barren, not to mention small. At the beginning of each universe's timeline, there is what one might call a "Little Bang": the explosion of a singularity, distributing mass that eventually coalesces into a single star, and one rocky planet orbiting that star. Neither one ever leads to the evolution of life.
From the outset, both universes are identical: their Little Bangs distribute their mass and energy in precisely the same configurations, leading to precisely identical rocky planets orbiting precisely identical stars. If you were to take a snapshot of either universe, exactly 100 petaseconds (about 3.17 billion years) from its beginning, you would see exactly the same picture. Each molecule, atom, and subatomic particle in universe X would have the exact same location, momentum, and physical properties as a corresponding particle in universe Y. Zooming out in either universe, you would see a star, orbited by a rocky planet, abundant in resources, cloaked in a gaseous atmosphere, located within the star's habitable zone, and devoid of life. Since cause always leads strictly to effect in each universe, then without any time travel, universes X and Y would continue to be identical forever: starting with identical initial conditions, and operating under identical, deterministic, no-time-travel physics, there would never be any possibility of divergence.
However, universes X and Y, though starting with identical initial conditions, and operating under identical, deterministic physics, do allow for the possibility of time travel. So it happens that, in universe X, 200 petaseconds from the beginning of time, certain travelers appear, arriving from decades in the future. An adult in middle age stands on the previously barren planet, carrying a baby in a sling, a bag well stocked with provisions, and several sheets of paper. Some of the pages contain schematics, diagrams, and notes, but most are devoted to a story, suitable for entertaining a young child as well as for provoking deep thought in an older child or adult. The adult quickly builds a rudimentary camp, sets the baby in bedding from their bag, and begins to gather resources from the surrounding area.
In universe Y, 200 petaseconds from the beginning of time, no travelers emerge, and the rocky planet continues to orbit its star uninhabited.
In universe X, a few days after the 200-petasecond mark — the moment of the travelers' arrival — the adult has established a routine that will allow them to sustain themself and the infant. Their species, which currently consists of two members, can acquire the nutrients they need from the minerals abundant on the planet's surface. The atmosphere regulates the planet's temperature, so that the days are warm but not too hot, and the nights are cool but not too cold. Each evening, at bedtime, the adult reads to the baby from the story, which the baby is still too young to understand.
In universe Y, a few days after the 200-petasecond mark — a moment of no particular significance — the rocky planet continues to orbit its star uninhabited.
In universe X, years pass, and the baby grows up while the adult grows older. They are still the only inhabitants of the rocky planet. The adult shares their knowledge and experience with the youth, and introduces them to the diagrams and schematics, which depict machines that the two can and must build together. The pair also discuss the implications of the story, always finding new angles of analysis.
In universe Y, years pass, and the rocky planet completes several orbits of its star, while nothing of note takes place on its surface. It is still uninhabited.
In universe X, dozens of years after the travelers' arrival, the younger of the two is now an adult, while the elder is growing too old to work. They have built one of the machines: a 3D printer, which can transform the resources of the planet into various useful tools and technologies. This will allow the other projects to move much faster and with less difficult labor, and the young adult feels confident in their ability to complete the other projects under the tutelage of their guardian. Their discussions of the story are more nuanced now, and both draw comfort from their ability to bond over familiar topics.
In universe Y, dozens of years after the universe's 200-petasecond anniversary, the rocky planet continues to orbit its star, uninhabited, looking much the same as it has for billions of years.
In universe X, fifty years after the rocky planet's settlement, all the machines are complete. Next to the printer stands a portal, capable of sending its user back in time, to the moment the universe was 200 petaseconds old. The third machine is also a printer of sorts, but much more specialized: given a sample of someone's genetic code, and enough raw material, it can produce an infant clone of the person whose genetics are used. The older of the two travelers lives long enough to see these machines come to fruition, but not much longer. They recall a particular line from the story, and recite it to their younger counterpart before slipping out of life. The survivor grieves.
In universe Y, 200 petaseconds plus fifty years into the universe's existence, the rocky planet continues to orbit its star uninhabited.
In universe X, the rocky planet's sole living inhabitant spends a year in contemplation. They print a new bag, a new sling, a pen, and sheets upon sheets of paper. They painstakingly copy each schematic and diagram by hand, down to the last detail. They immerse themself in the story, forced to slow down and take in its every word as they write it in fresh ink. They do not feel as lonely as they otherwise might. When the work is finally done, they know what comes next. A baby comes into the world, the first and only. The new bag is well stocked, and the new sling has an inhabitant. The last people in the world step through the portal.
In universe X, 200.00000161 petaseconds from the beginning of time, the rocky planet is once again uninhabited.
In universe Y, 200.00000161 petaseconds from the beginning of time, the rocky planet is as uninhabited as it has always been.
Neither universe will ever again sustain life. But they are no longer identical. On the surface of the rocky planet in universe X stand three technological achievements that will never again be used, near the resting place of the only person who ever lived. On a table lie schematics with no inventor and a story with no author. The planet's wind will eventually erode all of these to dust, but each mote will scatter to a different corner of the globe, adding a speck in one universe where there is none in the other. Meanwhile, the untouched resources of universe Y's rocky planet will follow their own trajectories, unaltered by the will of a living being. Their paths have irreversibly diverged from those of their counterparts.
There is no contradiction.