The Noahic Covenant was to Israel? That was a covenant with all creation. Israel according to the flesh didn't even exist yet!
The Abrahamic Covenant is to Israel? Gal 3 clearly says that the One who inherits the promises of that covenant is the Lord Jesus himself along with those who are united to Christ by faith.
The Davidic Covenant was to Israel? It was a covenant personally made to David that his son would sit on his throne and reign. Typologically fulfilled in Solomon and spiritually fulfilled in Christ.
The New Covenant is only for Israel? It is for all those who receive forgiveness through the shed blood of Christ.
The ONLY Covenant given to ONLY Israel was the Mosaic. And that Covenant has been fulfilled, completed, and vanished away.
And Romans 11 and Ephesians 2 clearly refute your idea that we are not an extension of faithful Israel. One tree, we've been grafted in. One new body, with the partition broken down.
I anticipated such an answer. Yes there were covenants before Abraham. We are not referring to those covenants.
The Bible does not contradict itself:
Romans 9:4 Who are Israelites; to whom
pertaineth the adoption, and the glory, and the covenants, and the giving of the law, and the service
of God, and the promises;
--The covenants pertain to Israel. They started with Abraham, the father of the Jewish nation.
Your other NT references simply support my view, or are taken out of context. There are only three references in the NT that refer to "covenants."
Romans 9:4--specifically to Israel.
Gal.4:24--specifically to the NT believer as I have already pointed out.
Eph.2:12--again referring to Israel, but a reference taken entirely out of context.
Gal.4:24: Paul is using an allegory.
Galatians 4:24 Which things
are an allegory: for these are the two covenants; the one from the mount Sinai, which gendereth to bondage, which is Agar.
--He specifically states that this is a figure of speech, a comparison.
It was Sarah and her promised seed that came to Jerusalem; It was Hagar and Ishmael that opposed them.
The law was given at Mount Sinai. Though holy, it could never be kept. The law was bondage. It could not set them free.
Now, Hagar and Ishmael were cast out. We are no longer under the law. We are made free from the law.
As Hagar brought forth a slave under the law, so Sarah brought forth a son, the child of promise.
We are heirs to that child of promise.
The promise is twofold. It is the promise of the millennial Kingdom,
It is a personal promise of a personal relationship with Christ. We are free from the law.
Ephesians 2:12 That at that time ye were without Christ, being aliens from the commonwealth of Israel, and strangers from the covenants of promise, having no hope, and without God in the world:
--I simply ask you to read this chapter carefully without prejudice.
He is writing to the local church in Ephesus. He is writing about unity.
He is writing to Jewish believers and Gentile believers. The Gentile believers indeed were without hope, alienated from Israel, and from the covenants, etc.
Now in Christ both Jewish believers and Gentile believers are one in Christ. The wall between THEM is broken down. There was to be no more prejudice, not more division. They were one in Christ.