The verses you offered by no means establish this assumption but require a Calvinist extrapolation out of context to all of the men I mentioned.
No it simply needs a further New Testament explanation of what was there in the OT.
John 3:10 Jesus answered and said to him, "Are you the teacher of Israel, and do not know these things?
Ellicott's Commentary for English Readers
“You who teach others, have you need to learn the very first lessons of true religion? You who claim to loose and bind men, and place heavy burdens on them which they cannot bear, are you without the simplest real knowledge of what God is, or of what man is? Do teachers of Israel know not these things when they lie beneath every page of the Old Testament Scriptures?”
Barnes' Notes on the Bible
As such a teacher he ought to have understood this doctrine. It was not new," but was clearly taught in the Old Testament.
Jamieson-Fausset-Brown Bible Commentary
The question clearly implies that the doctrine of regeneration is so far disclosed in the Old Testament that Nicodemus was culpable in being ignorant of it. Nor is it merely as something that should be experienced under the Gospel that the Old Testament holds it forth—as many distinguished critics allege, denying that there was any such thing as regeneration before Christ. For our Lord's proposition is universal, that no fallen man is or can be spiritual without a regenerating operation of the Holy Ghost, and the necessity of a spiritual obedience under whatever name, in opposition to mere mechanical services, is proclaimed throughout all the Old Testament.
Matthew Poole's Commentary
Our Saviour doth not so much wonder at as upbraid the ignorance of Nicodemus, and all of his sect, who went for masters, or teachers, and that in Israel; who had the law and the prophets, and yet were ignorant of those things which were necessary to be known to every ordinary person’s salvation. Will any say, But where was there any thing spoken in the books of the law and the prophets about regeneration, or a being born again?
Answer. What other things could be meant by the circumcision of the heart, commanded by Moses,
Deu 10:16, promised in
Deu 30:6; by the new heart, and the new spirit, promised
Ezekiel 36:26; by the clean heart prayed for by David,
Psalm 51:10? A teacher in Israel should from hence have understood the necessity of a new and of a clean heart; but the whole sect of the Pharisees were so taken up with the trifles of the rites and traditions, and the works of the law, that as to these spiritual things of nearer and much higher concernment to people’s souls, they knew and spake little of them.