I don't understand the distinction you draw between accepting faith as a gift of God and placed into the possession of its recipients - that being the equivalent of "jamming it down someone's throat"? I don't consider the receiving of such a wonderful gift as that - a gift in the truest sense, doesn't actually become a gift, until it comes into the receiver's possession. Neither do I believe that someone is pre-programmed before birth with faith, but rather, that it comes as a result of spiritual rebirth (being born again) upon salvation.
No one, until born-again and given faith, desires true faith. For to desire it, is to already have it. Faith, by definition, is antithetical to natural man, as it is un-acquirable through the efforts of natural man, it being dependent upon the mercy of God which is far beyond the understanding, power, and inclination of natural man.
Those saved - those whom by salvation are given faith - began from the condition of being dead in sin, unable to obtain true faith, blinded to the gospel. Had they not received it as an unsolicited gift, then they would not have been able to appropriate it at all. Yet, when it is received, it is so with joy unspeakable. Even though, so to speak, a gift "jammed down their throat", once it is received, its recipients become unwilling to forfeit or part with it because with it comes spiritual wisdom to realize what has been given them - the heart also becoming changed. Those to whom it is not given, will not be able to accept its true tenets, nor even desiring to accept them. Those who think they have obtained true faith of themselves - through their own efforts - by that, reveal they still lack true faith and an understanding of true faith.
[2Co 4:3-4 KJV]
3 But if our gospel be hid, it is hid to them that are lost:
4 In whom the god of this world hath blinded the minds of them which believe not, lest the light of the glorious gospel of Christ, who is the image of God, should shine unto them.