How did the people of the Old Testament know they had eternal life with God?

Jesus preached The Gospel of the Kingdom to the Jews.
Paul preached the Gospel of Grace to the Gentiles and said: But even if we, or an angel from heaven, preach any other gospel to you than what we have preached to you, let him be accursed. Galatians 1:8
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THE PROGRESSION OF SALVATION from Genesis to Revelation

In our progression of salvation we will see the Jewish Teaching of Jesus and the Gospel of the kingdom which is simplified to The Gentile Gospel of Paul which is Grace and Mercy.