Is God trying to save everyone now, in this age? Is this physical life the only chance a man or woman has to be saved? Traditional Christianity may teach this, but the Bible does not.
There is a future general resurrection of the dead. This is described for Israel in Ezekiel 37:1-14 and for the world in Revelation 20:11-15. At this time, all who have lived and died in this age who never had a chance for salvation will be given their first opportunity to hear the true gospel, to believe the gospel, to believe in Christ and accept Him as personal savior, and to repent and be baptized. Those who repent and accept Christ in faith will be forgiven and can receive the Holy Spirt and be converted and saved. This will include all the millions who lived and died before Christ was born who never knew about Christ and all the billions in many nations today who never had the opportunity to learn about Jesus Christ.
If God wanted to save everyone now, He would. All things are possible for God (Luke 18:27, Luke 1:37, Mark 10:27, Matthew 19:26). God is fully capable of making sure that the gospel is heard by every person on earth. But He has not done that.
Is a chance for salvation necessary in a general resurrection for those who never heard of Christ to be saved? Yes.
It is those who believe in Christ who will be saved (John 6:53-58, Acts 16:31, Romans 10:8-13, 1 John 5:9-13, Galatians 2:15-16, Acts 10:36-43, Acts 4:9-12, John 20:30-31, John 6:47), and it is necessary for those being saved to hear the gospel so they can believe it (Romans 10:14-15, Romans 1:16, 1 Corinthians 15:1-5, 2 Thessalonians 2:13-14, Luke 8:11-15, Acts 11:13-17, 1 Thessalonians 2:14-16, Acts 15:7-9). Yet billions in this life have never heard the gospel because of circumstances of birth and have had no opportunity to believe it and be saved.
In order to be saved, you must have the Holy Spirit of God (Romans 8:9-11). Notice in verse 11 that it is the Spirit of God dwelling in a Christian that gives life. It is those who are Christ's, that is, who have the Spirit of God who are raised to immortality at the second coming of Christ (1 Thessalonians 4:15-17, 1 Corinthians 15:23, 1 Corinthians 15:50-57). This is the first resurrection, the resurrection of the saints (Revelation 20:4-6).
Therefore, if a man does not have the Holy Spirit dwelling in him at the time of his death or when Christ returns, whichever comes first, he will not be in the first resurrection at the return of Christ, the resurrection to immortality.
But to receive the Holy Spirit, you must believe the gospel, repent, and be baptized in the name of Jesus Christ (Acts 2:38, Ephesians 1:13-14).
There were some who had repented and were living righteously, and were baptized into John's baptism, but had not received the Holy Spirit until they were baptized in the name of Jesus Christ, and only then did they receive the Holy Spirit (Acts 19:1-6). So the general rule is, without being baptized as a symbol of the acceptance of Jesus Christ, the Holy Spirit is not given. The millions in China and elsewhere who never had the opportunity to hear the name of Jesus Christ could not have been baptized in His name and therefore could not receive the Holy Spirit and therefore could not be in the first resurrection. Therefore, no matter how righteously they may live, they cannot be in the first resurrection. The only chance they will have is in the general resurrection described in Ezekiel 37.
Ezekiel 37:1-14 clearly shows that God will resurrection ancient Israelites who lived before Christ back to a second physical life on this earth and give them the opportunity to be saved. Notice, the dry bones Ezekiel sees are the whole house of Israel (Ezekiel 37:11), so this would include the men of ancient Israel who lived in Ezekiel's time and before, since they are part of the "whole" house of Israel. These people are brought back to physical life because muscle tissue is put upon the bones and breath must enter their bodies in order for them to live, according to Ezekiel 37:4-10. These are people who have died in the past and will come up out of their graves, according to Ezekiel 37:12-13. And God says He will put His Spirit in them, showing they can become converted and receive salvation (Ezekiel 37:14) because it is the Spirit of God that makes one belong to Christ (Romans 8:9, Acts 2:1-4, Acts 2:38).
Is it only Israel that is raised to life and given a chance for salvation? No. God does not show partiality based on nationality (Acts 10:34-35). All nations will be raised from the dead. Revelation describes this same event in Revelation 20:11-15. Notice that the book of life will be open (verse 12). Those who repent can have their names written in it.
God is love (1 John 4:8, 1 John 4:16, John 3:16-17) and God is very merciful (Exodus 34:6-8, Psalm 106:1, Luke 6:35-36, Hebrews 8:12, James 5:11). God does not want anyone to perish but for all to repent and be saved (2 Peter 3:9, 1 Timothy 2:3-4).
This is why there will be a general resurrection as described in Ezekiel 37 and Revelation 20. God in His mercy will give every human being who has ever lived a chance to hear the gospel and understand and a chance to believe the gospel, to repent, and to be saved. Those who do not have that opportunity in this life will be resurrected and given that opportunity in the general resurrection. Those who believe and repent can be saved, and those who reject the gospel after hearing it and understanding it will not be saved. God will not force His salvation upon anyone, and He will not take away our free will, but He will make sure everyone has the opportunity to hear the gospel and be saved.