With the inauguration of the New Covenant, God's covenant work turned to causing human beings to believe in His Son Jesus Christ:

Therefore they said to Him, "What are we to do, so that we may accomplish 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)

When one knows Jesus Christ, one meets and knows his personal God (John 14:7-11).

Jesus speaks of choosing His disciples including Judas Iscariot to fulfill His Father's plan:

I am not speaking about all of you. I know the ones whom I have chosen; but this is happening so that the Scripture may be fulfilled, 'He who eats My bread has lifted up his heel against Me.' From now on I am telling you before it happens, so that when it does happen, you may believe that I am He. Truly, truly I say to you, the one who receives anyone I send, receives Me; and the one who receives Me receives Him who sent Me." (John 13:18-20)

After the departure of Judas, Jesus reveals the purpose of choosing the disciples; they were chosen and appointed for fruitful service:

You did not choose Me but I chose you, and appointed you that you would go and bear fruit, and that your fruit would remain, so that whatever you ask of the Father in My name He may give to you. (John 15:16)

Jesus chooses Saul (who would be renamed Paul) to be His apostle to the Gentiles:

But the Lord said to him, "Go, for he is a chosen instrument of Mine, to bear My name before the Gentiles and kings and the sons of Israel; (Acts 9:15)

Correspondingly to Judas Iscariot, the apostle Peter indicates that God's choice of human beings includes non-Believers to carry out His covenant work:

The God of Abraham, Isaac, and Jacob, the God of our fathers, has glorified His servant Jesus, the one whom you handed over and disowned in the presence of Pilate, when he had decided to release Him. But you disowned the Holy and Righteous One, and asked for a murderer to be granted to you, but put to death the Prince of life, whom God raised from the dead, a fact to which we are witnesses. And on the basis of faith in His name, it is the name of Jesus which has strengthened this man whom you see and know; and the faith which comes through Him has given him this perfect health in the presence of you all. And now, brothers, I know that you acted in ignorance, just as your rulers also did. But the things which God previously announced by the mouths of all the prophets, that His Christ would suffer, He has fulfilled in this way. (Acts 3:13-18)

For deeper study:

What does the Greek verb "eklegomai" mean?