What does the Bible say? Does God predestinate? If so, to what extent?

Where shall I go from your Spirit?
Or where shall I flee from your presence?
If I ascend to heaven, you are there!
If I make my bed in Sheol, you are there!
If I take the wings of the morning
and dwell in the uttermost parts of the sea,
even there your hand shall lead me,
and your right hand shall hold me.
If I say, "Surely the darkness shall cover me,
and the light about me be night,"
even the darkness is not dark to you;
the night is bright as the day,
for darkness is as light with you.

For you formed my inward parts;
you knitted me together in my mother's womb.
I praise you, for I am fearfully and wonderfully made.
Wonderful are your works;
my soul knows it very well.
My frame was not hidden from you,
when I was being made in secret,
intricately woven in the depths of the earth.
Your eyes saw my unformed substance;
in your book were written, every one of them,
the days that were formed for me,
when as yet there were none of them.

Psalm 139:7-16

Here, David says that God saw him while he was still a formless embryo. Okay, God is omniscient. But he also says that God did the forming. In God's "book," that is, according to God's plan, he was formed. God had already planned in His wisdom how David would be formed in the womb.

Yet among the mature we do impart wisdom, although it is not a wisdom of this age or of the rulers of this age, who are doomed to pass away. But we impart a secret and hidden wisdom of God, which God decreed before the ages for our glory. None of the rulers of this age understood this, for if they had, they would not have crucified the Lord of glory. But, as it is written,

"What no eye has seen, nor ear heard,
nor the heart of man imagined,
what God has prepared for those who love him" -

these things God has revealed to us through the Spirit. For the Spirit searches everything, even the depths of God. For who knows a person's thoughts except the spirit of that person, which is in him? So also no one comprehends the thoughts of God except the Spirit of God. Now we have received not the spirit of the world, but the Spirit who is from God, that we might understand the things freely given us by God. And we impart this in words not taught by human wisdom but taught by the Spirit, interpreting spiritual truths to those who are spiritual.

The natural person does not accept the things of the Spirit of God, for they are folly to him, and he is not able to understand them because they are spiritually discerned. The spiritual person judges all things, but is himself to be judged by no one. "For who has understood the mind of the Lord so as to instruct him?" But we have the mind of Christ.

1 Corinthians 2:6-16

Paul says that the gospel is hidden from the rulers of this age (1 Corinthians 2:6). But we do not need to despair of some difficulty in the gospel for us. Why? Because God has decreed from eternity to reveal His gospel to us. This is our glory that we have the gospel revealed to us.

For those whom he foreknew he also predestined to be conformed to the image of his Son, in order that he might be the firstborn among many brothers. And those whom he predestined he also called, and those whom he called he also justified, and those whom he justified he also glorified.

Romans 8:29-30

Paul shows here that God has determined that all His adopted children will be conformed to the example of Christ. Our adoption and future glory are inextricably linked. Notice they are all in past tense. From God's perspective, they are so certain as to be rendered as good as done.

What shall we say then? Is there injustice on God's part? By no means! For he says to Moses, "I will have mercy on whom I have mercy, and I will have compassion on whom I have compassion." So then it depends not on human will or exertion, but on God, who has mercy. For the Scripture says to Pharaoh, "For this very purpose I have raised you up, that I might show my power in you, and that my name might be proclaimed in all the earth." So then he has mercy on whomever he wills, and he hardens whomever he wills.

You will say to me then, "Why does he still find fault? For who can resist his will?" But who are you, O man, to answer back to God? Will what is molded say to its molder, "Why have you made me like this?" Has the potter no right over the clay, to make out of the same lump one vessel for honored use and another for dishonorable use? What if God, desiring to show his wrath and to make known his power, has endured with much patience vessels of wrath prepared for destruction, in order to make known the riches of his glory for vessels of mercy, which he has prepared beforehand for glory - even us whom he has called, not from the Jews only but also from the Gentiles?

Romans 9:14-24

Paul here says that God has prepared the elect for glory. Before they are ever born, they are already destined to their lot.

Blessed be the God and Father of our Lord Jesus Christ, who has blessed us in Christ with every spiritual blessing in the heavenly places, even as he chose us in him before the foundation of the world, that we should be holy and blameless before him. In love he predestined us for adoption through Jesus Christ, according to the purpose of his will, to the praise of his glorious grace, with which he has blessed us in the Beloved. In him we have redemption through his blood, the forgiveness of our trespasses, according to the riches of his grace, which he lavished upon us, in all wisdom and insight making known to us the mystery of his will, according to his purpose, which he set forth in Christ as a plan for the fullness of time, to unite all things in him, things in heaven and things on earth. In him we have obtained an inheritance, having been predestined according to the purpose of him who works all things according to the counsel of his will, so that we who were the first to hope in Christ might be to the praise of his glory. In him you also, when you heard the word of truth, the gospel of your salvation, and believed in him, were sealed with the promised Holy Spirit, who is the guarantee of our inheritance until we acquire possession of it, to the praise of his glory.

Ephesians 1:3-14

We did not yet exist, so we could not have any merit, when this predestination occured. Our salvation comes from God alone. God predestined solely because it was His will to predestine us. He did this through Jesus Christ. And the end is the praise of his glorious grace.
Again, in verse 11, God works all things freely by His own will. Man brings nothing of his own to this equation. God looks no further than the counsel of His will.

But God, being rich in mercy, because of the great love with which he loved us, even when we were dead in our trespasses, made us alive together with Christ - by grace you have been saved - and raised us up with him and seated us with him in the heavenly places in Christ Jesus, so that in the coming ages he might show the immeasurable riches of his grace in kindness toward us in Christ Jesus. For by grace you have been saved through faith. And this is not your own doing; it is the gift of God, not a result of works, so that no one may boast. For we are his workmanship, created in Christ Jesus for good works, which God prepared beforehand, that we should walk in them.

Ephesians 2:4-10

Before we were born, God prepared good works. We cannot live a holy life in our own strength. We must be formed and transformed by God's own hand. God's grace came first, so we have nothing to boast. God owes us nothing. Any good we do is just a gift from God's treasures.
When Peter preached at Pentecost, he said,

this Jesus, delivered up according to the definite plan and foreknowledge of God, you crucified and killed by the hands of lawless men.

Acts 2:23

God from all eternity, did, by the most wise and holy counsel of His own will, freely, and unchangeably ordain whatsoever comes to pass; yet so, as thereby neither is God the author of sin, nor is violence offered to the will of the creatures; nor is the liberty or contingency of second causes taken away, but rather established.

Although God knows whatsoever may or can come to pass upon all supposed conditions; yet has He not decreed anything because He foresaw it as future, or as that which would come to pass upon such conditions.