It's important to latch on to covenant-concepts as they originate from the beginning, being articulated in the first book of Holy Scripture, Genesis. There is a crucial covenant-making ceremony in Gen.15, which should not be detached from God's first special interactions with Abraham going back to Gen.12, or the seal he puts on his covenant in Gen.17 through the sign of the covenant (circumcision); or even further to his affirmation of the promise of the covenant in the aftermath of the binding of Isaac, Gen.21, including assurance that the covenant will continue intergenerationally.
The covenant with Abraham isn't the first appearance either of the word for covenant in Genesis, or of the elements comprising covenant arrangements. We should avoid the word-concept fallacy, that alleges such-and-such is not to be recognized unless a particular term is used to describe the phenomenon. For this reason, looking back into the very beginning in Eden, we re-read God's interaction with Adam with the covenant concepts we read explicitly later on; and we recognize the stipulations of covenant formulae are plainly there in the garden. Israel, upon receiving Genesis from Moses' hand, and with their own experience at Sinai immediate in their minds, would doubtless hear the first man's experience through their own covenant experience filter.
This combination of hearing/reading and experience reinforces repeatedly the act of engagement with "my" text. Solidarity with the original parties, with the fathers of them inheriting the text containing the covenant, who understand the covenant is not just with them of the past (Dt.5:3) but with a new generation--these factors bring a present day reader into an understanding that God's covenant is in the word, and is the word. In fact, the very language we commonly use to refer to the Bible's main divisions demonstrates this: "Testament." This word is translated from the Gk "diatheke," which is rendered in the NT as either covenant or testament, and perhaps (some argue) should always be rendered covenant. When we consider that the Word was made flesh in Christ, we further connect our covenant identity to both the record of covenanting, to the record as covenant itself, and to the embodiment of covenant fulfillment and refreshment in the ideal covenant Man, the Lord Jesus.
Apostle Paul and other NT writers answer for us the important question of how Abraham's covenant (Gen.15) relates to the covenant at Sinai (Ex.24). They are related, but they are not the same. There are aspects of Israel's constitutional national covenant that have a strong "works" flavor (even if we guard against interpreting Sinai as if it was meritorious in essence). St. Paul writes that the later covenant, with its works content, could never supersede the earlier covenant (with Abraham) that was strictly promissory, Gal.3:17. St. Paul regards the NT believer, regardless of his genetic ancestry, as the heir of Abraham's covenant, Gal.3:29, Rom.4:11-12, downplaying the privilege of mere birth-connection, Rom.2:28-29. St. Paul is so bold as to register those who prefer Sinai to Jerusalem/Moriah as actually identifying with Ishmael over Isaac, Gal.4:21ff.
Apostle Peter invokes the Abrahamic covenant in Act.2:36-39, to reassure and to reinstate those cut-off from the covenant through murder of the Heir (cf. Mt.21:38-41), by faith in him who God raised from the dead. The "promise" (v39) is the foundational covenant made with Abraham, now realized in Christ, the true Heir of all his father's possession, Mt.28:18; cf. Gen.24:26. St. Peter uses the same terminology as God did of old, in order to awaken hope that salvation was not beyond them, and that in spite of everything they had done they might still be called "friends of God," Is.41:8; 2Chr.20:7; Jas.2:23.
The book of Hebrews has been called "the epistle of the covenant [diatheke]," because of how it fleshes out the Christological fulfillment of the faith of Abraham and of Israel. Christ is portrayed as the fulfillment of the covenant ideal, as the perfect Mediator, better than David, better than Aaron, better than Moses; the true King, Priest, and Prophet for the people. Abraham acted in mediatorial fashion back in Genesis. Moses was the mediator of the Sinai covenant, in which capacity he functioned in a way no successor would or could (filling all three covenant offices) until a Mediator of the New Covenant should arrive. Moses warned the people not to despise him when he arrived, Dt.18:15. Moses works for Jesus, and not the other way, Heb.3:3, 5-6.
Heb.9:18 states: covenant (making) and blood go together, see also Lk.22:20 and Heb.12:24. The New Covenant sees all that went before fullfilled. The Old Covenant that passes away is specifically Moses' covenant ("not like the covenant I made... bringing them out of Egypt," Jer.31:32) . It too is fulfilled along with everything in the Old Testament (which contains more than the Old Covenant). Christ is a better fulfillment to Abraham than even Isaac, who does take over his father's mediatorial roles (see Gen.26), and carries on the covenant life, to be passed on eventually to Jacob, etc. Christ is a better fulfillment to David and the special covenant promises made to him (Ps.89:28) than even Solomon, Mt.12:42. As a sign of New Covenant reality, Christ pours out the Spirit, Act.2, that was expected by the prophets (e.g. Jol.2:28) and which Moses could not do but longed to see, Num.11:29. The wonderful sign of Spirit-endowment was only tasted by a relative few in the pre-New Covenant era, by those prophets, priests, and kings who typified the One who was to come.
The passages you have been encouraged to read by me and the others responding in this thread are not the scripture PROOFS of covenant theology, that are bound convince the open-minded reader of how accurate CT must be. They are simply key texts that highlight how we think the Bible is meant to be read, cover to cover. Personally, I think once it is seen, it cannot be unseen. When/if that happens, these (and other) passages will appear as most abundant proofs of your conviction.