John 1:13 (King James Version)
"Which were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God."
John Calvin appears to have no problem with the mystery his later followers feel they must deny.
John Calvin on John 1:13
"The will of the flesh and the will of man appear to me to mean the same thing; for I see no reason why flesh should be supposed to signify woman, as Augustine and many others explain it. On the contrary, the Evangelist repeats the same thing in a variety of words, in order to explain it more fully, and impress it more deeply on the minds of men. Though he refers directly to the Jews, who gloried in the flesh, yet from this passage a general doctrine may be obtained: that our being reckoned the sons of God does not belong to our nature, and does not proceed from us, but because God begat us willingly, (James 1:18,) that is, from undeserved love. Hence it follows, first, that faith does not proceed from ourselves, but is the fruit of spiritual regeneration; for the Evangelist affirms that no man can believe, unless he be begotten of God; and therefore faith is a heavenly gift. It follows, secondly, that faith is not bare or cold knowledge, since no man can believe who has not been renewed by the Spirit of God.
It may be thought that the Evangelist reverses the natural order by making regeneration to precede faith, whereas, on the contrary, it is an effect of faith, and therefore ought to be placed later. I reply, that both statements perfectly agree; because by faith we receive the incorruptible seed, (1 Peter 1:23,) by which we are born again to a new and divine life. And yet faith itself is a work of the Holy Spirit, who dwells in none but the children of God. So then, in various respects, faith is a part of our regeneration, and an entrance into the kingdom of God, that he may reckon us among his children. The illumination of our minds by the Holy Spirit belongs to our renewal, and thus faith flows from regeneration as from its source; but since it is by the same faith that we receive Christ, who sanctifies us by his Spirit, on that account it is said to be the beginning of our adoption.
Another solution, still more plain and easy, may be offered; for when the Lord breathes faith into us, he regenerates us by some method that is hidden and unknown to us; but after we have received faith, we perceive, by a lively feeling of conscience, not only the grace of adoption, but also newness of life and the other gifts of the Holy Spirit. For since faith, as we have said, receives Christ, it puts us in possession, so to speak, of all his blessings. Thus so far as respects our sense, it is only after having believed -- that we begin to be the sons of God. But if the inheritance of eternal life is the fruit of adoption, we see how the Evangelist ascribes the whole of our salvation to the grace of Christ alone; and, indeed, how closely soever men examine themselves, they will find nothing that is worthy of the children of God, except what Christ has bestowed on them."