The OT covenant was based on birth to Jewish parents, the NT covenant is based on faith in Christ. Infants can't do that.
Nope. Kindly said, you are dead wrong. You don't know covenant and you have no idea how a covenant works. The principles of a covenant are the same, whether for the Old Covenant, the New Covenant, or even marriage. There are five basic principles of covenant upon which the covenant works. You can remember them by this acronymn:
T -- Transcendence (Who's in charge here?)
H -- Hierarchy (Rulership or authority)
E -- Ethics (What are the rules of the covenant?)
O -- Oaths and Sanctions (Vows taken upon making covenant/consequences of breaking covenant)
S -- Succession (The covenant continues from generation to generation)
You will find this in the Suzerainty kingship covenants of the Middle East, the Covenant of God, and even the Covenant of Marriage. If any one of these five principles is missing, it ain't a covenant.
Under Hierarchy, it is the father who is the "Covenant Head" over the family. Therefore, when a child is brought into the covenant, the faith of the faither as ruler, authority, and head over the household, is counted as the faith of the child. This is why a male baby could be circumcized at the age of 8 days old and was made fully member of the covenant community (aka "the Church") with all due priviledges and responsibilities under that relationship. It was the duty of the father to catechize his sons and daughters into the ethics of the covenant relationship with God and warn them of the dangers of breaking the covenant. You can see an example of covenant oaths/sanctions in Deuteronomy 28: 15-68. In like manner, it is the responsibility of fathers (and mothers) to catechize their children regarding the oaths/sanctions which were taken for that child as an infant, for like it or not, that child is a child of the covenant and is bound under those rules.
Hierarchy is the same principle of representation by which the high priest made Yom Kippur for the nation of Israel once a year. And it is the same principle by which the high priest condemned national Israel to death because he, in condemning Christ to death, acted for the entire nation of Israel. It is also the same principle by which Christ, acting as the eternal Great High Priest, represents the people of God in performing an eternal Yom Kippur in the "tabernacle not made with hands" in the heavenlies. (Hebrews 9:11). Under the principle of hiearchy, He is the Covenant Head of the New Covenant and represents the people of God.
This is really not your fault. Baptists are dispensationalists and are clueless regarding the covenant. I once hear my Anabaptist pastor tell a fellow parishioner "Covenant theology? Stay away from that. That's dangerous stuff."
Yeah, I guess it was. My friend went on to leave Emmanuel Baptist Church and become a Calvinist (they are deeply covenantal in their theology - at least, the conservative ones like Gary Sutton, etc.). The same understanding led me out of Protestantism and into the apostolic faith because when I really got into studying the principles of covenant, I couldn't find them anywhere in Protestantism of any flavor.
Every doctrine believed by Orthodoxy and shared by Roman Catholics can be defended from a covenantal viewpoint, especially that one that drives Protestants wild - the Queenship of the Theotokos and the honor we give her. If you want to understand it thoroughly, you can (shameless plug here) buy my book on the Covenant of God:
https://www.amazon.com/Dance-Isaiah...ds=patrick+seamus+ohara&qid=1624397447&sr=8-1
Not expensive at all, but it will show you what I found when I really dug into covenant and began to understand it.