Plot

Lewis (Daniel Hansen/Jordan Fry), is an aspiring young inventor who was left at an orphanage by his mother when he was an infant. He tries to show off his inventions to parents who come to se him but one goes wrong when a nut allergy comes up. He has yet to be adopted and fears that he never will be especially since he is almost thirteen and it's hard for teens to be adopted. Convinced that his birth mother will want him, he attempts to invent a memory-scanning machine in the hopes that he can find her. He spends all of his time on the project, causing his roommate Mike Yagoobian (Goob) to stay awake for days. This makes Goob fall asleep during his important little league game.

At Lewis' school science fair, Lewis is approached by a mysterious boy named Wilbur Robinson (Wesley Singerman), who claims to be a "time cop" from the future. Wilbur says that a man wearing a bowler hat has stolen a time machine that Wilbur wishes to recapture. The sinister 'Bowler Hat Guy' (Stephen Anderson), sends Doris (Ethan Sandler), his robotic bowler hat with mechanical arms, to sabotage Lewis' memory-scanner. As Lewis begins demonstrating the use of his machine, it explodes, throwing the science fair into chaos. Lewis runs out, and the Bowler Hat Guy steals his unattended memory scanner. Wilbur tells Lewis to go back to the science fair and fix the machine. To prove suspicious Lewis that he is from the future, Wilbur takes him to a flying time machine to take them to year 2037, thirty years forward.

While giving Lewis a tour of the world of the future, Lewis realizes he can use the time machine to go back and see his mother. Wilbur insists he go back to fix the memory scanner, and while arguing, they crash the time machine. Wilbur asks Lewis to fix it, and Lewis agrees under the condition that Wilbur takes him back to visit his mother afterward. Wilbur tries to hide Lewis in the garage of his house, but Lewis leaves and meets Wilbur's grandfather, Bud (Steve Anderson). Bud takes Lewis on a tour of the house, during which Lewis meets the rest of the fun-loving and overly-eccentric Robinson family. Wilbur explains that his father, Cornelius, the only member of the Robinson family that Lewis did not meet, invented several futuristic inventions earlier seen, including the time machines coining the motto "Keep moving forward". Despite being provided with blueprints, Lewis is unable to repair the time machine.

Meanwhile, Bowler Hat Guy and Doris follow Wilbur and Lewis to the future and attempt to kidnap Lewis so he can show them how his memory scanner works after failing to demonstrate it at InventCo. Meanwhile, the Robinsons offer to adopt Lewis but change their mind when they discover that he's from the past. Lewis runs away in misery after finding out Wilbur lied to him about going back to see his mom and encounters the Bowler Hat Guy, who lures him into his time machine by promising to bring him to his mother.

Lewis shows the Bowler Hat Guy how to operate his memory scanner in a dark room, but the latter goes back on his word and ties him up. Lewis questions what the Bowler Hat Guy has against him. He reveals that Lewis is Cornelius Robinson, making Wilbur his son and the Robinsons his family. As Lewis grapples with the revelation, he repeats his previous question. The Bowler Hat Guy flips on a light, revealing that they're in Lewis' old room at the orphanage, or as he claims their old room. He reveals himself as an aged and deeply embittered Mike Yagoobian (Goob). He tells Lewis that he is to be blamed for the miserable life of Goob, having kept him sleep-deprived, causing him to lose his little league game. Goob obsessed over this defeat, scaring away his chances at adoption, and stayed at the orphanage after it closed down, eventually coming to blame Lewis for his misery. Goob initially intended to get revenge by vandalizing Robinson Industries, only to meet DOR-15 (Doris), a failed and abandoned invention of Cornelius'. They cooperate to steal the time machine, able to steal it because Wilbur forgot to lock the garage door, and plotted to use it to capture and plagiarize Lewis's first famous invention, to ruin Lewis's career as an inventor. Lewis warns that their actions may drastically alter the future, but Goob doesn't care. Lewis tells his old friend that he should just let go of his past and "Keep Moving Forward", incidentally reciting his future motto. However, Goob finds it more convenient to blame Lewis.

Goob and Doris prepare to present the stolen invention to InventCo in the past. Wilbur and his robot Carl (Harland Williams) save Lewis and the memory scanner and escape. As they make their way back to the Robinson house, Lewis punches Wilbur in the shoulder for failing to lock the garage door, revealing that he knows he's his father. Then suddenly, Doris destroys Carl and steals back the memory scanner, returning to Goob as their time machine vanishes. The scenery around Lewis and Wilbur (still in the future) darkens, and Wilbur vanishes into oblivion as history is being rewritten. Lewis enters the derelict house and discovers the memory-scanner in the garage. Viewing its records, he discovers that after mass-producing the memory-scanner, Goob also mass-produces Doris, whereupon the multitude of robotic hats took control of their wearers, something Goob hadn't planned. The Robinsons' Utopian future is replaced by a Doris-controlled, smog-darkened industrial empire, with mankind reduced to slaves.

Pursued by an army of DOR-15 hats, Lewis manages to repair the time machine and uses it to go to the precise moment and location where Goob signs the contract at InventCo. Lewis causes Doris to disappear into oblivion by promising that he will never invent her. Lewis then shows Goob the bleak future Doris would have created, which is transformed before their eyes back into the Utopian future. After they land near the Robinson house, Wilbur is brought back into existence. Lewis gets Wilbur to offer for the Robinsons to adopt Goob (after he hit Goob with karate), but Goob, ashamed of what he has done, hides and then walks off uncertain of what to do.

Cornelius (Tom Selleck) returns from his business trip and panics upon discovering the time machines to be missing before meeting his younger self. Cornelius shows Lewis his lab and points out the memory scanner, the invention he was most proud of. He reminds Lewis that the future is never set in stone and what matters is what he does in the present. Wilbur fulfills his promise to Lewis by visiting the moment at which his mother abandoned him. Lewis nearly interrupts her from leaving the infant "him" but stops, choosing his Robinson future over a childhood with his mother.

Finally, Lewis returns to his own time and prevents Goob from becoming the Bowler Hat Guy by waking him up in time to catch the ball that lets him win the game. Lewis then returns to the science fair and demonstrates his memory scanner on the science fair judge, Dr. Krunkelhorn (Laurie Metcalf), revealing that she is Lewis' adopted mother, Lucille. Lewis also meets a young Franny, who desires to make frogs sing. Bud and Lucille adopt Lewis, who nickname him Cornelius, and sets to work building Carl in an observatory bought by Bud and Lucile, which becomes the Robinson house one day. Just before Lewis/Cornelius drives off with Bud and Lucille, he turns around and waves at Goob, who is also leaving the orphanage with his own new family. Bud and Lucille move into the house Lewis saw further in time where he continues his inventing, fulfilling his future.

The film ends by showing a quote by Walt Disney: "Around here, however, we don't look backwards for very long. We keep moving forward, opening up new doors and doing new things, because we're curious... and curiosity keeps leading us down new paths."