[Question] Acts 4:12 tells us, "And there is salvation in no one else; for there is no other name under heaven that has been given among men by which we must be saved." How, then, can people from Old Testament times and those in New Testament times, who have died without ever hearing the gospel, receive salvation?

[Answer] God gave each person an opportunity to receive salvation. This is the "judgment of conscience" (Romans 2:14-15). God selected the people of Israel, gave them the Law, and set them apart as the standard of salvation. If they lived by the Law, they would receive salvation; if they failed to live by the Law, they would not receive salvation. However, this could not be applied to the Gentiles, all those who are not the people of Israel. Therefore, for the Gentiles, their acting in goodness according to their conscience became a standard of the Law.
The heart of man is divided among the truthful heart God gave him, the untruthful heart that entered him by way of sin, and conscience that distinguishes the good from the evil (Romans 7:22-23). As conscience is formed by each individual, it can vary in accordance with the nature of heart with which he or she was born and the background in which he or she grew up. No matter how good one's conscience may seem, it cannot be compared to the absolute standards set forth by God.
The God of love, however, has shown His mercy and kindness by allowing salvation through the "judgment of conscience" to people who did not know the Lord. On the one hand, if people behaved in goodness and shunned evil according to their conscience, God recognized them to have obeyed the Law. On the other hand, if people knowingly shunned goodness and readily welcomed evil into their lives, it was as though they had disobeyed the Law and thus they had nothing to do with salvation.
Good-natured people believe in the existence of a god merely by looking upon the universe and everything created therein (Romans 1:20). They fear the heavens and make every effort to live good and righteous lives. If such people in the past had heard the gospel, they would have readily accepted the Lord. When their life in this world expired, God led them to the Upper Grave first and allowed them to hear the message of salvation and accept Jesus Christ.
Prior to His resurrection, Jesus preached the message of salvation for 3 days in the Upper Grave (1 Peter 3:19). This was a time for people who had received salvation by way of the Law from Old Testament times or the judgment of conscience to accept Jesus as their Savior. Afterwards, they were moved to a waiting place on the edges of the Paradise. People from New Testament times who received salvation through the judgment of conscience likewise hear the gospel and accept the Lord in the Upper Grave, and are moved to the waiting place. As Jesus Christ is the only path to salvation, even people who receive salvation by way of the judgment of conscience must go through this process.
Therefore, people who died without hearing the gospel in Old Testament times will receive salvation through the Law and the judgment of conscience, and in New Testament times through the judgment of conscience.