How do we know the story of Abraham and Sarah teaches about the gospel?

In Galatians 4:24, Paul classifies the story of Abraham, Sarah, and Hagar as an allegory, indicating that these historical events reveal deeper theological truths about the covenants. The birth of Isaac, a child of promise, represents believers under grace, while Ishmael, born of the flesh, symbolizes those under the law. Paul's interpretation affirms that all events in the Old Testament point to the gospel, showing that understanding scripture requires seeing how it foreshadows and culminates in Christ’s redemptive work.