As I have pointed out that link is not really exegetical. It's based on assumptions from word etymology that don't stand a critical analysis of the breadth of use of the term in the First Century. The allusion is not definite.
1 John 5:1 is quite definite. It says faith is based on new birth. John uses the same term, and puts new birth before those attributes dependent on it. John uses the words in his Gospel (and there are reasoned, if controversial, observations linking 1 John with his Gospel and not as a separate letter). What would put a meaning to John's words other than what he said? We're not extending an etymology argument to get here. We're only working from the Greek words John uses.
That seems quite a leap, as new birth hasn't been linked to this term for regeneration -- which is dizzyingly broad, as I've mentioned before, which would contradict any attempt to place a time precedence based on its use.
John 3 doesn't necessarily refer to baptism, and it's not linked to Titus 3 except by a more tenuous thread of concepts. The words are different; their meanings are different; the conclusions aren't coming through this linkage.
Being born again comes first according to 1 John 5:1.
Which comes first, archierieus: faith or repentance?
As I haven't seen an exegetical connection among more than a couple of the verses you cited, I didn't see the need to establish the case. But I'd point out some fairly obvious things here, with word uses in the Septuagint that are much more strongly associated than Titus 3 is to John 3.
The connection between Ezek 11 and Jer 31 was understood and analyzed in Judaic thought in Jesus' time.
These two passages connect with Jesus' ministry through the use of:
new covenant
heart change / new heart
poured-out Spirit
forgiveness of iniquity
Paul makes a comparison in 2 Cor 3 between a ministry written on stone and one written on the human heart that is interestingly parallel with the words used in Ezekiel 11.
And of course the writer of Hebrews cites the Jeremiah passage directly as the new covenant (Heb 8:13).
The connections are more numerous than the tentative proposal from Titus 3. This one's stronger.
I did not see an exegetical connection between 1 Jn 5:1 and Lk 3, Acts 2, Acts 3 etc. There is no place here where repentance precedes conversion/new birth. In Luke 3 in particular the baptism is a baptism of repentance, not of new birth. If baptism indicates new birth, then baptism and repentance pretty clearly
correspond to one another in Luke's wording. Acts 2 and 3 again bring repentance and baptism into correspondence with one another. In fact check out Acts 3:19 in comparison with 22:16.
The concepts of new life and conversion coincide; in your citations one doesn't precede the other. The precedence of one or the other has not been established by these references.
As for Romans 6:1-7, the resurrection of Christ didn't begin His spiritual life, so the connection there is lost in the illustration. Keep in mind that baptism is used as a picture of something happening internally. Once again, the timing doesn't correspond. If Christ's spirit didn't already have eternal life in the sense we're discussing, He wouldn't have survived the Crucifixion.
As for Jn 3 I'm fine with the connection there. But there's a difference between "water" and baptism.
1 John 5:1 continues to state its direct assertion that being born of God is precedential to belief. To try to promote these other verses into something they don't say explicitly -- that they really don't say at all -- and then oppose that to the open statement of John -- that seems less tenable. An open statement of Scripture, is it more to be trusted than an implicit inference from word order?
Everyone who believes that Jesus is the Christ has been born of God
It's actually not a parallel in John 1 -- a different parallel is explicitly stated. And in fact the right to become sons of God is not the parallel of "born of God" in John 1:12.
But to all who did receive him, who believed in his name, he gave the right to become children of God, who were born, not of blood nor of the will of the flesh nor of the will of man, but of God.
From the construction of this sentence, "who received him" and "who were born" occupy the same grammatical roles. They're the parallels. This sentence doesn't really establish strong parallels.
Again -- is an arrogated parallel to override the explicitly-stated parallel of Scripture?
"kai"/"and" is not explicit evidence of temporal sequence. If it did, then we'd be looking at other verses where repentance precedes belief, and confession precedes belief.