This is impossible. One can not be "born again" into the spirit until all sin is removed. One must be "justified (declared righteous) before this happens. thus one must be Justified before they are born again.
since justification comes through faith, faith must come first. and as said so correctly. Faith comes by hearing. Do we hear what the HS is telling us, or do we reject.
Jesus explains it clearly in John 6.
36 But I said to you that you have seen Me and yet do not believe. 37 All that the Father gives Me will come to Me, and the one who comes to Me I will by no means cast out. 38 For I have come down from heaven, not to do My own will, but the will of Him who sent Me. 39 This is the will of the Father who sent Me, that of all He has given Me I should lose nothing, but should raise it up at the last day. 40 And this is the will of Him who sent Me, that everyone who sees the Son and believes in Him may have everlasting life; and I will raise him up at the last day.”
How do we see and believe jesus? he explained this too.
vs 61 -63 When Jesus knew in Himself that His disciples complained about this, He said to them, “Does this offend you? What then if you should see the Son of Man ascend where He was before? It is the Spirit who gives life; the flesh profits nothing. The words that I speak to you are spirit, and they are life.
Faith (trust) comes by hearing, which comes by the spirit (who teaches the natural man) we have two choices. Believe and be saved. Reject and not be saved, But have no excuse (romans 1)