Jesus never said one word about the New Testament. Despite the big red letters that say "New Testament of our Lord" on an otherwise blank page in front of Matthew, the New Testament didn't begin until Pentecost. Nobody in the gospels was born again. The new birth was not available until Pentecost. If the NT and new birth were available when Jesus was here, why did he have to die?The Jews received the gospels first. Jesus preached the New Covenant to them. That was different from the Old Covenant and why the Pharisees hated Him. When they finally rejected Jesus, then Peter saw a vision of the unclean meat (Leviticus 20:25-26) being cleansed so the gospel could now go to them and they are grafted into Israel's tree whose roots are Jesus.
Peter's vision occurred after Pentecost. prior to that, the Gentiles were flat out of luck.
Eph 2:11-12,
11 Wherefore remember, that ye [being] in time past Gentiles in the flesh, who are called Uncircumcision by that which is called the Circumcision in the flesh made by hands;
12 That at that time ye were without Christ, being aliens from the commonwealth of Israel, and strangers from the covenants of promise, having no hope, and without God in the world:
12 That at that time ye were without Christ, being aliens from the commonwealth of Israel, and strangers from the covenants of promise, having no hope, and without God in the world: