In the Bible heaven is God’s space while earth (or, if you like, ‘the cosmos’ or ‘creation’) is our space. And the Bible makes it clear that the two overlap and interlock. For the ancient Jews, the place where this happened was the temple; for the Christians, the place where this happened was Jesus himself, and then, astonishingly, the persons of Christians because they, too, were ‘temples’ of God’s own spirit.
Hawking is working with a very low-grade and sub-biblical view of ‘going to heaven.’ Of course, if faced with the fully Christian two-stage view of what happens after death—first, a time ‘with Christ’ in ‘heaven’ or ‘paradise,’and then, when God renews the whole creation, bodily resurrection—he would no doubt dismiss that as incredible. But I wonder if he has ever even stopped to look properly, with his high-octane intellect, at the evidence for Jesus and the resurrection? I doubt it—most people in England haven’t. Until he has, his opinion about all this is worth about the same as mine on nuclear physics, i.e. not much.