....Is there any Biblical evidence that Abraham was "regenerated"? NO.
And he believed in Jehovah; and he reckoned it to him for righteousness. Gen 15:6
Was it Abraham's belief that made him righteous, or did his belief show him to be righteous?
Was it an unrighteous man, that Jehovah called out of Mesopotamia years earlier, appeared to several times, and announced blessings upon? I think not.
Was it an unregenerate man that built an altar to Jehovah at Shechem years earlier? I think not.
Was it to a dead alien sinner that Melchizedek pronounced 'Blessed be Abram of God Most High' years earlier? I think not.
Abraham's faith showed him to be righteous; it did not make him righteous. YES, there is much biblical evidence that Abraham was regenerated EXACTLY in the sense that Luke is defining it.
But he that doeth the truth cometh to the light, that his works may be made manifest, that they have been wrought in God. Jn 3:21
Where does faith come from?
So then faith cometh by hearing, and hearing by the word of God. (Romans 10:17)
This passage is frequently mis applied. The context of the chapter is concerning Israel after the flesh. Dare to take it to the next verse:
But I say,
Did they not hear? Yea, verily, Their sound went out
into all the earth, And their words
unto the ends of the world. Ro 10:18
How is one born again?
Being born again, not of corruptible seed, but of incorruptible, by the word of God, which liveth and abideth for ever. (1 Peter 1:23)
If you're making this the written word then how is your stance any different than that of the Jews?:
Ye search
the scriptures, because
ye think that in them ye have eternal life; and these are they which bear witness of me; Jn 5:39
The scriptures do not convey eternal life, they bear witness of Christ. Paul reiterates this here:
..........our Saviour Christ Jesus, who abolished death, and brought life and immortality to light through the gospel, 2 Tim 1:10
The gospel does not impart life and immortality, it tells of it. And those that believe the gospel show by their faith that they have been born from above:
He that believeth on the Son hath eternal life;......Jn 3:36
.....He that heareth my word, and believeth him that sent me, hath eternal life,...Jn5:24
... He that believeth hath eternal life. Jn 6:47