In the future, humanity uses time travel to construct Eternity, an organization "outside time" which aimed to improve human happiness by observing human history and, after careful analysis, directly making small actions that cause "reality changes", as well as to help establish trade between the various centuries to help those in most need. Its members, known as "Eternals" and by the roles they hold, prioritize the reduction of human suffering, at the cost of a loss to technology, art, and other endeavors which are prevented from existing when judged to have a detrimental effect. Those enlisted travel "upwhen" and "downwhen" and re-enter time in devices called "kettles". Their rules prevent them from earlier travel to the Primitive times before the 27th century, when the temporal field powering Eternity was established, to prevent accidental damage to pre-temporal history. Also, humanity's fate is unknown – the earth is empty by the 150,000th century, but this is preceded by a period called the Hidden Centuries from the 70,000th–150,000th centuries in which for unknown reasons they cannot access the world outside Eternity to learn more.

Andrew Harlan is an Eternal and an outstanding Technician – a specialist at implementing reality changes – who is fascinated by the Primitive times. Senior Computer Laban Twissell, the Dean of the Allwhen Council, enrolls him to teach a newcomer, Brinsley Sheridan Cooper, about the Primitive. Harlan's teaching is interrupted with a short assignment which requires him to stay for a week in the 482nd century with non-Eternal Noÿs Lambent, a member of the aristocracy of that time. Harlan falls in love with her, and discovers that in the new reality planned for that time, she does not exist. Against Eternal laws, he removes her from time and hides her in the empty sections of Eternity that exist in the Hidden Centuries.

Harlan later finds that the kettles will not travel to the time he hid Noÿs (there is a block at the 100,000th century), and confronts Assistant Computer Finge with a weapon, accusing him of sabotaging matters out of jealousy. Finge states he has reported Harlan's conduct, and did not place the block. Harlan is summoned to the Council but is not reprimanded; he deduces that because his transgressions were ignored, he must be there to serve a larger purpose. Harlan confronts Twissell and explains that he has been teaching himself temporal mathematics and believes that its 23rd century inventor, Vikkor Mallansohn, must have been helped in his discovery by someone from his future; he concludes that his current role is training Cooper to do this. Twissell confirms this, adding that unknown to Cooper, Mallansohn's secret memoirs show that Cooper will take over Mallansohn's role and in effect, become Mallansohn. This must be kept from Cooper, so that Eternity will be founded as it historically was. Harlan blackmails Twissell by threatening to destroy Cooper's ignorance unless Noÿs is returned, but is outwitted; Twissell locks him in the control room with all controls deactivated other than the lever to send Cooper back – matching the memoir's statement that this was his role. Harlan, enraged, breaks open the controls and changes the power output, causing Cooper to be sent back to an unknown point estimated to be in the early 20th century.

Twissell is aghast, but as Eternity still exists, he theorizes he can undo Harlan's damage, and send Cooper back correctly for his mission. They think Cooper might try to communicate using an advertisement in one of Harlan's Primitive magazines that would only stand out to an Eternal. Harlan finds a magazine from 1932 has changed, and now shows an advert in the form of a mushroom cloud, something no human could have known of in 1932. However, Harlan refuses to tell Twissell about the advertisement until they bring Noÿs back from the Hidden Centuries, which he had been previously barred from him with a barrier at the 100,000th century, which Twissell insists is theoretically impossible. Together, they travel far upwhen to discover what has happened. Twissell speculates that the Hidden Centuries might be a time when humans evolved and changed into something else. They pass the 100,000th century unhindered and find Noÿs. Harlan agrees with Twissell that he will travel downwhen and bring back Cooper, so he can be sent to the correct time for his mission – but only if Noÿs comes with him.

On arrival in 1932, Harlan holds Noÿs at gunpoint, revealing that he suspects her of being from the Hidden Centuries, and that he has brought her so that she could not harm Eternity. Noÿs acknowledges she is from that time, and explains that her people had also developed time travel but their method shows many possible futures rather than just one future as seen by Eternity. They learned that humans would have been the first species to spread into the universe, but in each future where Eternity existed, safety was given a priority and by the time humans reached the stars, other species predominated and prevented this. In each future, humanity died out afterwards, in a species-wide depression. Noÿs' mission was to make the minimum change to history to remedy this – which was to prevent Eternity from ever being founded. There were multiple ways of achieving this, and she chose an approach in which she and Harlan were together. Noÿs gives Harlan the choice of killing her and preserving Eternity, or letting her live and allowing a different future to arise. Harlan, remembering the unhealthy interpersonal relationships between the Eternals, and the sociological damage he has seen done to people whose original "homewhen" had ceased to exist, begins to agree with her. Suddenly, a reality change occurs; the kettle disappears, indicating that Eternity now never happened. The book ends by stating that this was "the end of Eternity – and the beginning of Infinity".

JDW might have to choose between his mission to save the world/human existence or Elizabeth Debicki's character.
I still have a hunch that North by Northwest meets inception rumor is somewhat true. Comparison to North by Northwest is maybe due to the fact that Elizabeth Debicki's character betrays Kenneth Branagh for the love interest of JDW. And the comparison to Inception is obvious, not that it's related to the Inception universe but due to its mind-bending structure like inception.