There will be two distinct groups occupying the Earth during the millennial kingdom—those with glorified bodies, and those with earthly bodies who lived through the tribulation and on into the millennial kingdom. Those with glorified bodies consist of the Church, receiving glorified bodies at the rapture (1 Thessalonians 4:13-18; 1 Corinthians 15:21-23, 51-53), and those who are resurrected after Christ returns to Earth (Revelation 20:4-6). Those who have earthly bodies can be subdivided into two groups: believing Gentiles and believing Jews (Israel).
In Revelation 19:11-16, we find the return of Jesus Christ to Earth, known as His second coming. The rapture (1 Thessalonians 4:13-18; 1 Corinthians 15:51-53) is an appearing of Christ in the air, not His second coming. I mention this to make a distinction between the rapture and the second coming of Christ. There is no mention in Revelation 19-20 of any kind of rapture event. The implication is that saints who are on Earth when Christ returns will remain on Earth to enter the millennial kingdom in their natural bodies. If the rapture or any kind of event where a living believer receives a glorified body were included in the second coming of Christ to Earth, one would expect to find reference to such a major event in Revelation 19. But no such reference is to be found. The only event that results in believers receiving glorified bodies is found in Revelation 20:4-6 where those who became believers during the Tribulation and were killed because of their faith are resurrected. It is also believed that at this same time Old Testament saints will be resurrected, also receiving glorified bodies (see Daniel 12:2).
Matthew 25:31-46 is another passage that should be considered. This passage is commonly called the separation or judgment of the sheep and the goats. The sheep and goats refer to righteous and unrighteous Gentiles. Christ will judge the unrighteous Gentiles (goats), and they will be cast into the lake of fire for eternal punishment (Matthew 25:46). Therefore, no unbelieving Gentile will survive to live on into the millennial kingdom. The righteous Gentiles, or sheep, will live on into the millennial kingdom. They will give birth to children and will populate the Earth. However, these are not the only ones who will be producing children during the millennial kingdom.
The impression is given that when Christ returns, all Israel will trust in Him (Zechariah 12:10). They, too, will not receive glorified bodies (as did those who were raptured prior to the tribulation and those resurrected afterward). They also will produce children during the millennial kingdom.
So, believing Gentiles, Israel, and resurrected/raptured believers (all of whom have glorified bodies) will occupy the Earth. It should be noted, however, that believers with glorified bodies will not be reproducing. There is no marriage after this life (Matthew 22:30).
Children born during the millennial kingdom will have the responsibility of faith in Christ as all people of past ages have (faith in Christ since His coming; faith in God before—Genesis 15:2-6; Habakkuk 2:4; Romans 3:20). Unfortunately, not all of the children that are born during the millennial kingdom will come to faith in Christ. Those that do not will be led away by Satan into rebellion against God at the end of the millennial kingdom when Satan is let loose for a short time (Revelation 20:7-10).