No, it's not clear at all- a few mental gymnastics are required to make it fit your interpretation in fact. And it would be a bit redundant anyway for our Lord to tell us that one must be born physically first, and then spiritually. The first assertion would be too obvious to bother with.
Thank you for for opinion-and it's a novel one. I don't know off hand of any early fathers, having, as they did, a greater vantage point than any of us today in terms of knowing the faith that was passed down from the earliest disciples, who would agree with you. So here's the opinion of a few of them, but realize that the full list is very long, with similar understandings among many, many fathers.
“As many as are persuaded and believe that what we teach and say is true, and undertake to be able to live accordingly, and instructed to pray and to entreat God with fasting, for the remission of their sins that are past, we pray and fast with them. Then they are brought by us where there is water and are regenerated in the same manner in which we were ourselves regenerated. For, in the name of God, the Father . . . and of our Savior Jesus Christ, and of the Holy Spirit , they then receive the washing with water. For Christ also said, ‘Unless you are born again, you shall not enter into the kingdom of heaven’ ” (Justin Martyr, First Apology 61 ).
“‘And dipped himself . . . seven times in the Jordan’ . It was not for nothing that Naaman of old, when suffering from leprosy, was purified upon his being baptized, but as an indication to us. For as we are lepers in sin, we are made clean, by means of the sacred water and the invocation of the Lord, from our old transgressions, being spiritually regenerated as newborn babes, even as the Lord has declared: ‘Except a man be born again through water and the Spirit, he shall not enter into the kingdom of heaven’” (Irenaeus, Fragment 34 ).
“No one can attain salvation without baptism, especially in view of the declaration of the Lord, who says, ‘Unless a man shall be born of water, he shall not have life’” (Tertullian, Baptism 12:1 ).
“The Father of immortality sent the immortal Son and Word into the world, who came to man in order to wash him with water and the Spirit; and he, begetting us again to incorruption of soul and body, breathed into us the Spirit of life, and endued us with an incorruptible panoply. If, therefore, man has become immortal, he will also be God. And if he is made God by water and the Holy Spirit after the regeneration of the laver he is found to be also joint-heir with Christ after the resurrection from the dead. Wherefore I preach to this effect: Come, all ye kindreds of the nations, to the immortality of the baptism” (Hippolytus, Discourse on the Holy Theophany 8 ).
