I am a non-Calvinist, I believe in once saved, always saved, and that Christ died for all humanity, providing the means of salvation for all humanity.
Yes, I believe how we are raised influences how open we are to God's word. An obvious example, if you parents believed in Christ and raised you to believe in Christ, chances are you would start out inclined to believe in Christ.
On the other hand, say you were raised to believe in Islam, you would not be inclined to say Islam is a lot of hooey, and Christ is the way.
The NT tells us of people who were looking for the Messiah, and chose to believe Jesus was the Messiah. Thus they were open to God's word, and had not been taught to reject Christ.
All of us are pre-disposed to go our own way and not submit to the dictates of others, until we realize our way leads to pain, suffering and death. But we are still vulnerable to being taught Christ's way wrongly such that believe we are saved when we are not. See Matthew Chapter 7 for example.
The lost seem to be in a little more vulnerable state than the angels, as because of the Fall, the lost were made sinners, and are corrupted such that they are pre-disposed to sin.
I do not think the bible teaches our choice to trust in Christ is fully independent of our experience.
I do not think the bible teaches God predestined our every experience in life, as the bible says things happen by chance.
But the bible does teach that people who are not "of My sheep" will not put their trust in Christ. Others, however, who are open to God's word, might to some degree trust in Christ. These comprise the fields white with harvest for which we are to pray for more laborers.
In
Matthew 13 we have examples of four responses to the gospel. The first soil was so hardened he could not even understand the gospel. So prior experience certainly plays a part. The second soil liked good news, but did not fully commit to Christ as Savior and Lord, such that he had not root in himself. The third soil committed, making Christ a priority, but not his overriding priority.
Another verse impacting the OP question is the one where it says some plant, others water, but God causes the increase. Clearly human activity is said to provide exposure to the gospel, i.e. planting the seed, and the same or other humans water, which is to provide follow-up witnessing, both by words and by the way they live, exhibiting the fruit of the Spirit.
So the bible presents several "deciding factors" when it comes to responding to the gospel. Whether or not we are open to God's word, with some so hardened they cannot even comprehend the gospel. But someone very open to God's word who never has the gospel presented does not respond, God through direct or indirect revelation must reveal His gospel. Not to introduce controversy, but if a person is not drawn to Christ by His lovingkindness in dying for them, they are not among us, as
John 6:44 says. Scripture says Jesus demonstrated His love for us by dying for us when we were still sinners, and we love God because He first loved us.