Romans 8:28-30 says: And we know that in all things God works for the good of those who love him, who have been called according to his purpose. For those God foreknew he also predestined to be conformed to the image of his Son, that he might be the firstborn among many brothers and sisters. And those he predestined, he also called; those he called, he also justified; those he justified, he also glorified.

John 3:16 says: “For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life.”

The Bible does not contradict itself!  So how can we reconcile God’s predestination with our free will?

Overview:
Predestination means God predetermines outcomes.
His foreknowledge means He knows in advance what will happen, but what happens is nevertheless a result of His decisions.
Having decided the perfect outcome, He enables and causes the universe (in every detail and development) to produce that one outcome; in that sense it is indeed inevitable.
We are given the ability (individually) to produce God’s intended results (for us), principally to decide to accept God’s salvation, and therefore to be one of the “whoever” believes and has eternal life.
While we have freedom during “time” to choose for or against God’s plan, that plan is eternal, made before time, and will be achieved.
We will find, after making our personal decision, that it was God’s plan all along that we would do that!

These things are relatively easy to understand, since God is all-knowing and all-powerful.  But for us, with limited intellectual ability compared to God’s, the problem arises when we also consider what we call “free will”.
Scripture declares that “whosoever calls on the Name of the Lord shall be saved” (Rom.10:13). It also says that “Whoever comes to me, I shall not cast out” (Jn 6:37), and famously Jn 3:16 quoted above says God so loved the world that whoever believes shall not perish. In every case, this means the individual person makes the decision to be saved or not (and becomes accountable for that decision!).
Our problem is deciding who is really making the choice. If the free and final choice is indeed ours, then God is limited in what He can predestine; He can then only use His foreknowledge to see how we will decide and then, knowing who will decide to be saved He predestines those people (alone) be saved. But this robs “predestination” of its essential meaning and makes it pre-confirmation (of our decision, not His) instead!
But if we say God has already made up His mind who will be saved, then how can He hold people who are not saved accountable, since really they had no choice?
So we have two seemingly irreconcilable realities: (1) God does choose in advance who will be saved and (2) Each one of us gets to choose if we accept salvation or not.
Many books have been written that attempt to explain this dilemma. Some try to suggest God only pre-decides the conditions on which people will get saved, then individuals make the final choice (but God foreknew their decision anyway). Some similarly propose God’s predestination only deals with objectives (big picture: there will be a plan of salvation) not personal details, again leaving results to be determined by the free choice of individuals. Some (often termed Calvinists or hyper-Calvinists) instead say there is effectively no free choice for humans and God has pre-determined all results.   Scripture references may be quoted to support either conclusion.

So where does that leave us?
See if you find the following explanation satisfactory:
1. The Fall (Gen.3) is a reality, and means every human being deserves to be lost forever (Rom.3). God therefore foreknew that He would be committed to condemn ALL in perfect justice.
2. God not only has foreknowledge, so expected the Fall, He also has the capacity for ultimate mercy (Rom.11:32); He can in love save people who don’t deserve it (this would include of course, babies and mentally incapacitated and those who never hear the gospel, as well as the rest of us!).
3. If salvation was based simply on our decision, it would mean we are saved by our merit, BUT God’s plan ensures everyone who is saved is saved because of God’s mercy not their merit (Eph.2:8).
4. To satisfy God’s justice, the penalty for sin must still be paid, and in God’s plan it is paid by Him. By paying it Himself, He is gloriously righteous in being merciful to those who are delivered from His judgment (Rom.3:26). But His righteousness is also glorified in condemning the guilty!
5. Since He pays fully for the salvation, He has the perfect right to decide/choose who gets saved (Rom.9:19-24).
6. If He disclosed in advance who is actually going to be saved, such disclosed inevitability would mean we would lose all incentive to seek to glorify Him in our lives and service (Satan would gloat!).
7. If He does not disclose to us who will be saved, that gives us a sense of urgency to preach the Gospel (Christ is glorified by the preaching!).
8. While if we were God we would logically make the identical choices about who to save and who to leave lost, we are NOT God and therefore should not question His decision or the exceedingly complex mechanics He uses to bring that decision about (the ‘algorithm’ if you like, that He chooses to use in perfectly balancing His justice with His mercy, including using preaching: 1 Cor.1:21!). All we know, with our limited human understanding, is that the outcome is the one that brings the most glory to Christ (Col.1).
9. If a person who is lost refuses God’s plan of salvation, saying “its God’s fault I’m lost because He has pre-decided that”, the person is simply acknowledging the reality of (1) above and choosing, entirely of their own volition and accountability, to ignore (4) above. We know this, because if they expressed any true desire to receive God’s mercy through Christ, God is committed definitely to save them (e.g. Jn 3:16). The ‘algorithm’ would have that result in that individual’s case.
10. Because we do not know the mechanics of God’s ‘algorithm’, this gives urgency to preaching and also to praying. We must pray for God’s righteousness to be seen, and never give up (Lk.18:1). We must pray with God’s desire that all should be saved (1 Tim.2:4). Prayer is, essentially and specifically, asking God to do what He knows is best, and to express agreement with His decisions; for this we need to be in a personal condition to recognize the out-working of His will.