“And this I say, that the covenant, that was confirmed before of God in Christ, the law, which was four hundred and thirty years after, cannot disannul, that it should make the promise of none effect”
The New Covenant did not start at the times of Jesus, it had always been in force, as the saints of old were justified by faith and not their works, as we can see in the main scripture above.
The question, however is, why was the law introduced if there was already righteousness by faith? Verse 19 of Galatians chapter 3 answers this question: “Why, then, was the law given at all? It was added because of transgressions until the Seed to whom the promise referred had come…”
The phrase ‘because of’ is better translated from the Greek as ‘to lead to’. This means that the law was given to cause transgressions. The law was referred to by Paul as the ‘ministration of condemnation’ and the ‘ministration of death’ in 2 Corinthians 3:9. It was introduced to show the Israelites that in their own power, they could not save themselves from the motions of sin.
The law was never designed to make man righteous, it was for the very opposite. The law came to point man to the only option for salvation – Christ!