First, where can you show that ANYBODY was ever saved "under the Old Covenant"???? I know of no one that obtained salvation "under" the Old Covenant? The Old Covenant could not convey life eternal according to Paul and "no flesh" has ever been justified under the old Covenant.
If N

NE can be justified/saved/etc. under the Old Covenant then what covenant were they saved under?
I suggest that all who were saved between Genesis and Pentecost were saved under "the blood of the EVERLASTING covenant" - Heb. 13:20
David was saved under the everlasting Covenant - 2 Sam. 23:5
Although my house be not so with God; yet he hath made with me an everlasting covenant, ordered in all things, and sure: for this is all my salvation, and all my desire, although he make it not to grow.
All individuals were saved under the everlasting covenant - Isa. 55:3
Incline your ear, and come unto me: hear, and your soul shall live; and I will make an everlasting covenant with you, even the sure mercies of David.
We are saved under the everlasting covenant - Acts 13:34
And as concerning that he raised him up from the dead, now no more to return to corruption, he said on this wise, I will give you the sure mercies of David.
This is the "EVERLASTING" covenant it is not a dispensational covenant or a temporary covenant or a covenant between Genesis and Acts, but the EVERLASTING covenant between Genesis and Revelation and the ONLY covenant of salvation ever given by God under which anyone can be saved.
The "old" versus the "new" covenants are merely EARTHLY ADMINISTRATIONS of the "everlasting covenant" (Heb. 9:1). The "old" emphasized the holiness of God by law which pointed to those who attempted and failed to keep the law to the gospel of the coming Christ (everlasting covenant) which was a primary JEWISH covenant, whereas the "new" covenant emphasizes the grace of God by emphasizng the fulfillment of the gospel promise (the everlasting covenant) which is primary a GENTILE covenant.