I am glad to see St. Augustine being pulled into the discussion. It is important to understand what he thought in his heart.
If we look at ST. Augustine's theology on salvation we find this: Wace and Piercy "A dictionary of Christian Biography"
In St. Augustine's letter to Deogratius (Ep. 102):
At all times, he writes, since the world began, the same faith has been revealed to men, at one time more obscurely, at another more plainly, as the circumstances altered; but what we now call the Christian religion is but the clearest revelation of a religion as old as the world. Never has its offer of salvation been withheld from those who were worthy of it even though they might not be mentioned in the sacred record. Such men who followed His commands (however unconsciously), were implicit believers in Christ. The changing (and therefore semi-real) form represents the one constant reality, the saving grace of God, revealed through the passion and resurrection of Christ (Ep 189 )
Now, here is the passage and below that an example of being drawn taken from the New Testament, and following that is St. Augustine's heartfelt understanding.
John 6:44: No man can come to me, except the Father which hath sent me draw him: and I will raise him up at the last day.
45 It is written in the prophets, And they shall be all taught of God. Every man therefore that hath heard, and hath learned of the Father, cometh unto me.
People are drawn to God through revelation. Here's an example:
Matthew 16:13-18 KJV: “When Jesus came into the coasts of Caesarea Philippi, he asked his disciples, saying, Whom do men say that I the Son of man am? And they said, Some say that thou art John the Baptist: some, Elias; and others, Jeremias, or one of the prophets. He saith unto them, But whom say ye that I am? And Simon Peter answered and said, Thou art the Christ, the Son of the living God. And Jesus answered and said unto him, Blessed art thou, Simon Barjona: for flesh and blood hath not revealed it unto thee, but my Father which is in heaven. And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it.”
According to St. Augustine (source: Tractates on the Gospel of John Tractate 26), emphasis mine:
4: Thence also He says here, if thou turn thy attention to it, “No man cometh to me except he whom the Father shall draw.” Do not think that thou art drawn against thy will. The mind is drawn also by love. Nor ought we to be afraid, lest perchance we be censured in regard to this evangelic word of the Holy Scriptures by men who weigh words, but are far removed from things, most of all from divine things; and lest it be said to us, “How can I believe with the will if I am drawn?” I say it is not enough to be drawn by the will; thou art drawn even by delight. What is it to be drawn by delight? “Delight thyself in the Lord, and He shall give thee the desires of thy heart.” Ps. xxxvii. 4. There is a pleasure of the heart to which that bread of heaven is sweet. Moreover, if it was right in the poet to say, “Every man is drawn by his own pleasure,”—not necessity, but pleasure; not obligation, but delight,—how much more boldly ought we to say that a man is drawn to Christ when he delights in the truth, when he delights in blessedness, delights in righteousness, delights in everlasting life, all which Christ is? Or is it the case that, while the senses of the body have their pleasures, the mind is left without pleasures of its own? If the mind has no pleasures of its own, how is it said, “The sons of men shall trust under the cover of Thy wings: they shall be well satisfied with the fullness of Thy house; and Thou shalt give them drink from the river of Thy pleasure. For with Thee is the fountain of life; and in Thy light shall we see light”? Ps. xxxvi. 8. Give me a man that loves, and he feels what I say. Give me one that longs, one that hungers, one that is traveling in this wilderness, and thirsting and panting after the fountain of his eternal home; give such, and he knows what I say. But if I speak to the cold and indifferent, he knows not what I say. Such were those who murmured among themselves. “He whom the Father shall draw,” saith He, “cometh unto me.”
5: But what is this, “Whom the Father shall draw,” when Christ Himself draws? Why did He say, “Whom the Father shall draw”? If we must be drawn, let us be drawn by Him to whom one who loves says, “We will run after the odor of Thine ointment.” Cant. (Song of Songs) i. 3. But let us, brethren, turn our minds to, and, as far as we can, apprehend how He would have us understand it. The Father draws to the Son those who believe on the Son, because they consider that God is His Father. For God begat the Son equal to Himself, so that he who ponders, and in his faith feels and muses that He on whom he has believed is equal to the Father, this same is drawn of the Father to the Son. . . . One whom the Father has drawn says: “Thou art Christ, Son of the living God.” Not as a prophet, not as John, not as some great and just man, but as the only, the equal, “Thou art Christ, Son of the living God.” See that he was drawn, and drawn by the Father. “Blessed art thou, Simon Barjonas: for flesh and blood hath not revealed it to thee, but my Father who is in heaven.” Matt. xvi. 16, 17. This revealing is itself the drawing.