Although I believe that salvation is all of God from beginning to end, and I believe that eternal security is all of God and none of us, I do believe that one's salvation is not independent of means (the foolishness of preaching), nor independent of hearing the gospel, nor independent of repentance and faith.
I think where you and I see things differently is related to when and how one acquires the ability and the will to believe, as well as the basis of God's choice of his chosen.
I agree that salvation is not independent of means. Although I believe an unregenerate man has the ability to believe, he
must have an object of faith. You cannot possibly believe in something you have never heard of and have no knowledge of.
And this is what Paul meant when he asked "and how shall they believe in whom they have not heard?" Isn't this why we send missionaries deep into the jungles? Not because those men have no ability to believe a truth when they hear it, but because they have never heard of Jesus Christ.
Paul never even remotely implies that a man has no ability to believe truth when he hears it, he says they must hear the Word of God, they must hear of Jesus before they can believe in him.
And this is the problem with believing a person must be regenerated to have the ability to believe. Having the ability to believe is not enough, you must also have an object of faith to believe in. This is knowledge.
I posted several times from R.C. Sproul's assistant where he said infants can be regenerated for years before they trust on Christ.
The problem here is that you would have a person who is born again, a person who has everlasting life that is not a believer. An infant cannot possibly trust in Jesus because they have no knowledge of him, and no ability to understand the gospel. So you have a born again unbeliever!
And we are justified by faith, even a Calvinist believes that. So, if an infant can be regenerated, then you not only have a person with everlasting life who is not a believer, but they are still in their sins!
Oh, the Calvinists will say that the moment you are regenerated you also have faith (but they will always insist regeneration occured first). You still have a major problem. It is not enough to have the ability to have faith. You must know the gospel. You must know and realize you are a sinner. You must know and realize that Jesus Christ is the Son of God who died for our sins and rose from the dead. This is absolutely impossible for an infant to know, and yet many Calvinists teach that an infant can be regenerated for many years before they acquire this knowledge to trust in Christ.
If so, then a person can be born again and have everlasting life when they are not a believer, and when they are in all their sins.
Do you see how this doctrine is absurd and totally unscriptural?
Here is a statement where it is shown some believe infants can be regenerated by the Holy Spirit.
XIII. Second proposition: "Although infants do not have actual faith, the seed or root of faith cannot be denied to them, which is ingenerated in them from early age and in its own time goes forth in act (human instruction being applied from without and a greater efficacy of the Holy Spirit within)." This second proposition is opposed to the Anabaptists, who deny to infants all faith, not only as to act, but also as to habit and form. Although habitual faith (as the word "habit" is properly and strictly used to signify a more perfect and consummated state) is not well ascribed to them, still it is rightly predicated of them broadly as denoting potential or seminal faith. Now by "seed of faith," we mean the Holy Spirit, the effecter of faith and regeneration (as he is called, 1 Jn. 3:9), as to the principles of regeneration and holy inclinations which he already works in infants according to their measure in a wonderful and to us unspeakable way. Afterwards in more mature age, these proceed into act (human instruction being employed and the grace of the same Spirit promoting his own work by which that seed is accustomed to be excited and drawn forth into act).
Do you understand what this is saying? It is admitting that infants can not fully trust in Christ because they do not have knowlege to trust in Christ. Nevertheless, they teach that infants can be regenerated by the Holy Spirit and enabled to believe so that when they are mature enough and do hear the gospel years later will believe.
So, as I said, you would have a born again person with everlasting life who is not a believer and is still in all their sins.