you don't go straight to heaven when you die; you go into the grave. God will raise the dead on doomsday. Those who believed in him will then go to heaven. Those who never heard of him (you don't have to go back to Neanderthals, there are plenty of people around today who know nothing of Christianity) will be resurrected to physical life, and will be given 1000 years to repent and qualify for salvation. It's in Revelation 20, should you want to look it up: "the rest of the dead did not live again until the thousand years were finished."