Only the New Covenant is the Covenant of Grace. OT saints were saved the same way we are today: by New Covenant union with Christ. This concept is not baptist eisegesis. Here are a variety of quotes affirming this truth (I’ll add to it as I come across more).
Christ can work out of that finished work in the future because it has been decreed and ordained. So the Holy Spirit can be active according to ordo salutis even in advance of the historia salutis pouring out.Camden Bucey, Christ the Center 700 Redemption Accomplished and Applied
J.V. Fesko, The Trinity and the Covenant of Redemption, 347
Old Testament believers enjoyed the benefits of union with Christ and His imputed righteousness prior to His earthy ministry. The covenantal-legal agreement of the pactum [i.e., the Covenant of Redemption] was sufficient in and of itself due to the Trinity’s utter trustworthiness to carry out its covenant-oaths. In other words, the stipulations of the pactum, an inherently legal arrangement, are the foundation for the application of redemption in covenant of grace.
Calvin (Commentary Hebrews 8:10)
[W]hatever spiritual gifts the fathers obtained, they were accidental as it were to their age; for it was necessary for them to direct their eyes to Christ in order to become possessed of them… There is yet no reason why God should not have extended the grace of the new covenant to the fathers. This is the true solution of the question.
Horton, Rediscovering the Holy Spirit, p152ff (See extended quote here: Horton’s Retroactive New Covenant)
There are clear passages indicating that ‘the forgiveness of sins’ is unique to the New Covenant (“remember their sins no more”; Jer 31:34)… Kuyper seems to confirm this conclusion. He argued that the energies of the Spirit at Pentecost worked retroactively in the lives of OT saints.
John Frame, Systematic Theology, p. 79-81 (See extended quote here John Frame’s Retroactive New Covenant)
[T]he work of Christ is the source of all human salvation from sin: the salvation of Adam and Eve, of Noah, of Abraham, of Moses, of David, and of all of Godâ’s people in every age, past, present, or future. Everyone who has ever been saved has been saved through the new covenant in Christ. Everyone who is saved receives a new heart, a heart of obedience, through the new covenant work of Christ. So though it is a new covenant, it is also the oldest, the temporal expression of the pactum salutis… The New Covenant does have a temporal inauguration… the shedding of Jesus’ blood, a datable historical event, is the substance of the New Covenant, the Covenant that purifies, not only the flesh, but the conscience, the heart. Nevertheless, as we saw earlier, the efficacy of the New Covenant, unlike that of previous covenants, extends to God’s elect prior to Jesus’ atonement. When believers in the Old Testament experienced “circumcision of the heart,” or when they were Jews “inwardly,” they were partaking of the power of the New Covenant.
Augustine, A Work on the Proceedings of Pelagius, 189 (See more quotes here)
[T]he happy persons, who even in that early age [the Old Testament] were by the grace of God taught to understand the distinction now set forth, were thereby made the children of promise, and were accounted in the secret purpose of God as heirs of the New Testament; although they continued with perfect fitness to administer the Old Testament to the ancient people of God.
Augustine, A Treatise Against Two Letters of the Pelagians, 406-407 (See more quotes here)
These pertain to the new testament [covenant], are the children of promise, and are regenerated by God the Father and a free mother. Of this kind were all the righteous men of old, and Moses himself, the minister of the old testament, the heir of the new . . . Let us, therefore, choose whether to call the righteous men of old the children of the bondwoman or of the free. Be it far from us to say, of the bondwoman; therefore if of the free, they pertain to the new testament [covenant] in the Holy Spirit, whom, as making alive, the apostle opposes to the killing letter. For on what ground do they not belong to the grace of the new testament [covenant]?
Aquinas Summa Theologica I-II, 106-107 (See more here and here)
[A]lthough the Old Law contained precepts of charity, nevertheless it did not confer the Holy Ghost…
the New Law is chiefly the grace itself of the Holy Ghost, which is given to those who believe in Christ…
Nevertheless there were some in the state of the Old Testament who, having charity and the grace of the Holy Ghost, looked chiefly to spiritual and eternal promises: and in this respect they belonged to the New Law…
As to those under the Old Testament who through faith were acceptable to God, in this respect they belonged to the New Testament: for they were not justified except through faith in Christ, Who is the Author of the New Testament…
No man ever had the grace of the Holy Ghost except through faith in Christ either explicit or implicit: and by faith in Christ man belongs to the New Testament. Consequently whoever had the law of grace instilled into them belonged to the New Testament… at all times there have been some persons belonging to the New Testament, as stated above.”
Catechism of the Catholic Church, quoting Aquinas (1964)
There were . . . under the regimen of the Old Covenant, people who possessed the charity and grace of the Holy Spirit and longed above all for the spiritual and eternal promises by which they were associated with the New Law… [E]ven though the Old Law prescribed charity, it did not give the Holy Spirit, through whom “God’s charity has been poured into our hearts.”
Nehemiah Coxe, Covenant Theology from Adam to Christ (75)
The grace and blessings of the new covenant were given and ensured to Abraham for himself.
Keach, “The Display of Glorious Grace” in The Covenant Theology of Benjamin Keach (Conway: Free Grace Press, 2017), 110.
All believers, who lived under the Old Testament, were saved by the covenant of grace, which Christ was to establish.
These things being observed, we may consider that the Scripture doth plainly and expressly make mention of two testaments, or covenants, and distinguish between them in such a way, as what is spoken can hardly be accommodated unto a twofold administration of the same covenant… Wherefore we must grant two distinct covenants, rather than a twofold administration of the same covenant merely, to be intended… If reconciliation and salvation by Christ were to be obtained not only under the old covenant, but by virtue thereof, then it must be the same for substance with the new. But this is not so; for no reconciliation with God nor salvation could be obtained by virtue of the old covenant, or the administration of it, as our apostle disputes at large, though all believers were reconciled, justified, and saved, by virtue of the promise, whilst they were under the covenant… This covenant thus made, with these ends and promises, did never save nor condemn any man eternally. All that lived under the administration of it did attain eternal life, or perished for ever, but not by virtue of this covenant as formally such… [T]herefore I have showed in what sense the covenant of grace is called “the new covenant,” in this distinction and opposition… The greatest and utmost mercies that God ever intended to communicate unto the church, and to bless it withal, were enclosed in the new covenant. Nor doth the efficacy of the mediation of Christ extend itself beyond the verge and compass thereof; for he is only the mediator and surety of this covenant.Owen (Exposition, Hebrews 8:6, 9)