How were old testament prophets like Abraham and those who lived in China, India, or Samaria saved?
They were saved by faith, just like we are. In Romans 4:3 Paul wrote, “Abraham believed God and it was credited to him as righteousness.” He was speaking about a righteousness from God that’s imputed to us by faith. The message of the cross is as old as Genesis and through out history every believer has looked to the cross for salvation. In the Old Testament they looked forward. In the New Testament we look back.
It’s important to remember that at the beginning everyone believed in God, and in His promise to redeem them from their sins. As men were scattered from Babel to populate the Earth, they took the knowledge of a coming Redeemer with them. Many rejected the message, just like they do today. But a there was always a remnant who believed and no matter where they went their faith sustained them and ultimately saved them.