"1 Cor. 7 But we speak the wisdom of God in a mystery, the hidden wisdom which God ordained before the ages for our glory, 8 which none of the rulers of this age knew; for had they known, they would not have crucified the Lord of glory. 9 But as it is written: "Eye has not seen, nor ear heard, Nor have entered into the heart of man The things which God has prepared for those who love Him." 10 But God has revealed them to us through His Spirit. For the Spirit searches all things, yes, the deep things of God. 11 For what man knows the things of a man except the spirit of the man which is in him? Even so no one knows the things of God except the Spirit of God. 12 Now we have received, not the spirit of the world, but the Spirit who is from God, that we might know the things that have been freely given to us by God. 13 These things we also speak, not in words which man's wisdom teaches but which the Holy Spirit teaches, comparing spiritual things with spiritual. 14 But the natural man does not receive the things of the Spirit of God, for they are foolishness to him; nor can he know them, because they are spiritually discerned. 15 But he who is spiritual judges all things, yet he himself is rightly judged by no one. 16 For "who has known the mind of the Lord that he may instruct Him?" But we have the mind of Christ.

Only the spiritual man, the man (or woman) with new life, one who is a new creation in Christ, can experience the things of God and know the things God has prepared, and understand the deep things of God.

We cannot understand the things of God any other way than through and by our spirits, and by having the spirit of wisdom and revelation. College degrees, intelligence, etc, cannot give us spiritual revelation and understanding.

The word "natural" here comes from the Greek word translated "soul." Hence it means "soulish," if such were an English word. The soulish man cannot see the things of the spiritual realm. The aspects of the soul, like the intellect, cannot enter in the mysteries of the Kingdom. These things have to be revealed spiritually.
The spiritual man is alive to God in spirit, soul, and body. The natural man is dead to God spiritually. He cannot know God, because his spirit is dead. Eternal life is to know God, and his Son.

These things are to be taught, NOT in words which man's wisdom teaches ("total depravity," "active obedience," "trinity," etc) but are to be taught using words which the Holy Spirit teaches - the form of sound words.

But the Word can convict and awaken a lost soul, and because the Word carries faith, they can throw themselves at Christ and receive new life. They can look unto him and be saved. How does this work. I don't know. I only that this is the way the bible says it.

How does man get this new nature?

The scripture answers that we become a spiritual man when we receive spiritual life:

11 In Him you were also circumcised with the circumcision made without hands, by putting off the body of the sins of the flesh, by the circumcision of Christ, 12 buried with Him in baptism, in which you also were raised with Him through faith in the working of God, who raised Him from the dead.

The new nature is to put off the flesh and be raised again in Christ through the faith of the operation of God.

This comes by believing and receiving the gospel:
22 Since you have purified your souls in obeying the truth through the Spirit in sincere love of the brethren, love one another fervently with a pure heart, 23 having been born again, not of corruptible seed but incorruptible, through the word of God which lives and abides forever,

We agree that a natural man cannot have faith.
We agree that faith is a gift from God.

Yes, we agree that faith is not of the soulish part of man. Faith is the gift of God. It is carried by the Word.

We agree we must have faith to believe.
We agree that after we believe, we are saved.

Did you mean "to be saved"? Than yes we agree.

How does the natural man become a spiritual man?

By being born again. How? "To as many as RECEIVED him, to them he gave the right to be BORN children of God." John 1:10.

By coming to Christ and receiving life:

40 And this is the will of him that sent me, that every one which seeth the Son, and believeth on him, may have everlasting life: and I will raise him up at the last day. John 6:40

But whosoever drinketh of the water that I shall give him shall never thirst; but the water that I shall give him shall be in him a well of water springing up into everlasting life. John 14:14

Then Jesus said unto them, Verily, verily, I say unto you, Except ye eat the flesh of the Son of man, and drink his blood, ye have no life in you. John 6:53

Jesus said unto her, I am the resurrection, and the life: he that believeth in me, though he were dead, yet shall he live: John 11:25

But these are written, that ye might believe that Jesus is the Christ, the Son of God; and that believing ye might have life through his name. John 20:31

A natural, soulish man, can receive the Word, and believe it. Christ is still the true light which lights everyman that comes into the world, even in man's fallen condition. The grace of God which brings salvation has appeared to ALL men.

The passage in Corinthians is not speaking of how a person comes to Christ. The scripture is clear that we must come IN ORDER TO HAVE life.

And ye will not come to me, THAT YE MIGHT HAVE life. John 5:40

So, we must be changed before we can believe so that the spiritual things are not folly to us. God must give us ears to hear and eyes to see, and hearts that can believe or else we are dead to God.

How can a dead man hear? how can they hear the voice of the Son of God and be made alive? I don't know, but that is how it is:

"The hour is coming when the dead will hear the voice of the Son of God, and those who hear WILL live. For just as the Father has life in Himself, even so He gave to the Son also to have life in Himself. John 5:24-26

See that? Hearing first, then living. How? Don't know! Is it so? well, yes.

Hope that helps you to at least see where I am coming from even if you still think i am a stubborn heretic. Regards.