It is believed that Jesus will come back for the second time.
1 second after people: Heaven is overcrowded and Jesus sees that humanity is gone
1000 years after people: Jesus comes down to earth for his second coming. But with no humans around to see him, He goes back to heaven and uses a time machine to save the last humans from dying 1000 years ago.
Some point before humans became extinct: Jesus restores humanity and prevents it from becoming extinct.