In His commitment to His divine covenants, God provides the Messiah:

For God so loved the world, that He gave His only begotten Son, that whoever believes in Him shall not perish, but have eternal life. For God did not send the Son into the world to judge the world, but that the world might be saved through Him. He who believes in Him is not judged; he who does not believe has been judged already, because he has not believed in the name of the only begotten Son of God. (John 3:16-18)

Jesus sees faith as a command:

Therefore they said to Him, "What shall we do, so that we may work the works of God?" Jesus answered and said to them, "This is the work of God, that you believe in Him whom He has sent." (John 6:28-29)

The apostles understand a saving faith as an act of obedience:

Paul, a bond-servant of Christ Jesus, called as an apostle, set apart for the gospel of God, which He promised beforehand through His prophets in the holy Scriptures, concerning His Son, who was born of a descendant of David according to the flesh, who was declared the Son of God with power by the resurrection from the dead, according to the Spirit of holiness, Jesus Christ our Lord, through whom we have received grace and apostleship to bring about the obedience of faith among all the Gentiles for His name's sake, among whom you also are the called of Jesus Christ; (Rom 1:1-5)

Since you have in obedience to the truth purified your souls for a sincere love of the brethren, fervently love one another from the heart, for you have been born again not of seed which is perishable but imperishable, that is, through the living and enduring word of God. (1 Pet 1:22)

But Peter and the apostles answered, "We must obey God rather than men. The God of our fathers raised up Jesus, whom you had put to death by hanging Him on a cross. He is the one whom God exalted to His right hand as a Prince and a Savior, to grant repentance to Israel, and forgiveness of sins. And we are witnesses of these things; and so is the Holy Spirit, whom God has given to those who obey Him." (Acts 5:29-32)

As a contrast, unbelief is seen as disobedience:

He who believes in the Son has eternal life; but he who does not obey the Son will not see life, but the wrath of God abides on him. (John 3:36)

This precious value, then, is for you who believe; but for those who disbelieve, the stone which the builders rejected, this became the very corner stone, and, a stone of stumbling and a rock of offense; for they stumble because they are disobedient to the word, and to this doom they were also appointed. (1 Pet 2:7-8)

However, they did not all heed the good news; for Isaiah says, "Lord, who has believed our report?" (Rom 10:16)

For deeper study:

Does genuine repentance always lead to salvation?