I gave you the evidence. People can believe and be saved when God opens the door of faith to them, through the hearing of the word.
No that is not how it happens and the scriptures do not say it is so. The Lord decided the whole of the gentile world was now to be reached and started that. It was not for individuals. God wants all men to be saved and is calling all men. He does not enable some and not others to have faith. Faith is a choice a man makes. God is not giving them faith nor manipulating them. This is cruel.
Romans 10:14
And how can they believe in the One of whom they have not heard?
This is referring to hearing by people preaching. Notice Paul did not say "how can they believe in the One of whom they have not been infused with faith by him, unbidden?" He did not think God infuses faith into some or opens the door of faith but that men need to hear the Gospel when other men tell them that. Why is this not clear? Hearing is with the human ears, not God giving them suddenly special ears.
What you are doing is editing out the scripture you like so that it says what the author was NOT saying. This is really clear in the one you choose because the verses after say,
"How then can they call on the One in whom they have not believed? And how can they believe in the One of whom they have not heard? And how can they hear
without someone to preach?
15And how can they preach unless they are sent? As it is written: “How beautiful are the feet of those who bring good news!”
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Clearly this is mere mortal men sharing the gospel with other mortal man who come to believe it because of what it says. This has happened with a lot of people in the world. They hear the gospel and it makes sense and appeals to the heart that is weighed down with sin and they repent and are forgiven and believe. Yes God is involved in convicting sin and try to woe them, but He is not reaching inside and manipulating them so they have no choice.
When God calls...that's when you can be saved. That's when you can have the free will to believe and be saved and fulfill God's desire for you to be saved. Or, have the free will to not believe and fulfill God's will for the wicked to show the power of God's wrath.
No, no man is saved when God calls. A man is saved when he repents of his sin, asks forgiveness and is forgiven and surrenders his life to God. God calls a lot..many are called. But not all called are then saved. We all have free will all the time including free will to fulfill God's desire for us in many matters.
But this is really a strange view you have. A man has no free will but when God calls then suddenly he has "free will" to make one choice and one choice only." Reminds me of Russian election, "one man, one vote, one candidate" and you had better make that on voting day as there is no free will to refuse to vote at all. That is exactly what you are saying. We rightly see it as oppression and not freedom at all.
Why can't you accept that God gives man free choice to say yes or no and let it be at that. That is what is in scripture and real life. Jesus described the process and although in one case the Enemy steals away the Word, the others freely accepted at least for a time. He did not say God manipulated the ones receiving so that must accept the Word and have no choice or in your terms "suddenly have free will to say "yes" but no free will to say "no." This is not a good theology.