Jack Frost awakens from a frozen pond with amnesia. Upon realizing no one can see or hear him, he disappears. Three hundred years later Jack, as the spirit of Winter, enjoys delivering snow days to school kids, but resents that they don't believe in him. At the North Pole, the Man in the Moon warns Nicholas St. North that Pitch Black is threatening the children of the world with his nightmares. He calls E. Aster Bunnymund, Sandy, and Tooth, to arms. They are then told that Jack Frost has been chosen to be a new Guardian. Jack is unimpressed by this position, as he still resents not being believed in, but North convinces him to aid them.
Visiting Tooth's world, Jack learns that baby teeth contain memories and innocence of the children who lost them; Jack's teeth are included, but tells Tooth he doesn't remember. However, Pitch raids Tooth's home in order to kidnap all of her subordinate tooth fairies except Baby Tooth, whom Jack saved, so that the children's teeth can't be collected and steals all the teeth, thus preventing Tooth from sharing Jack's memories and causing children to not believe. In order to thwart Pitch's plan, the group decides to collect. During their journey, a quarrel between North and Bunnymund awakens a boy, Jamie. Since he believes, he can see all except for Jack. Pitch's nightmares then attack, provoking Sandy as the Guardian of Dreams. Jack aids, but Sandy is then killed by Pitch.
As Easter approaches, the dejected Guardians gather in Bunnymund's home. With the unexpected aid of Jamie's little sister, Sophie, they begin the process of painting eggs for Easter. After Jack takes Sophie home, he is lured to Pitch's lair by a voice. Pitch then taunts him with his memories and fear of non-belief, distracting him long enough for Pitch to destroy the eggs, causing children to stop believing in Easter and Bunnymund. Losing his trust to the Guardians, Jack isolates himself in Antarctica, where Pitch tries to convince him to join his side, but threatens to kill Baby Tooth unless Jack gives him his staff. He agrees, but Pitch breaks Jack's staff and throws him down a chasm. Unlocking his memories, he learns that he was a mortal teenager who fell into ice while saving his younger sister. Inspiring him, Jack fixes his staff and returns to the lair to rescue the kidnapped baby fairies.
Due to Pitch, everyone except Jamie disbelieves, weakening the Guardians. Finding Jamie's belief wavering, he makes it snow in his room, renewing belief and causing Jack to be seen and heard. Jack and Jamie gather his friends, whose renewed belief bolsters their fight against Pitch consecutively. Pitch unsuccessfully threatens them, but their dreams prove stronger, resulting in Sandy's resurrection. Defeated and disbelieved in, Pitch tries to retreat, but his nightmares cause him to be trapped in his lair. Afterward, Jamie and his friends bid goodbye to the Guardians as Jack accepts his place as the Guardian of Fun.

Question: How long after Jack awakes does he reappear?
Answer: Three hundred years
Alternative answer: Three hundred years.