Jeremiah 31:31 “Behold, the days are coming, declares the LORD, when
I will make a new covenant with the house of Israel and the house of Judah, 32
not like the [Moses’s Sinai] covenant that I made with their fathers on the day when I took them by the hand to bring them out of the land of Egypt, my covenant that they broke, though I was their husband, declares the LORD. 33 For this is
the covenant that I will make with the house of Israel after those days, declares the LORD:
I will put my law within them, and I will write it on their hearts. And I will be their God, and they shall be my people.
I see the context of Jer 31:31-33 verses as meaning that God did away with the Mosaic Covenant (the inferior law covenant, see 2 Cor 3:1-7 (esp v7)) with a superior covenant through Christ that fulfilled the promises made in the Abrahamic and Davidic covenants. Jer 31:33: This is the New Covenant in which GOD WILL put HIS law within "the House of Judah and Israel" (His true people the invisible Church)(via the Holy Spirit that guides us from within us) and I will write the letter [of the law] on their hearts.
Jer 31:34: And no longer shall each one teach his neighbor and each his brother, saying, ‘Know the LORD,’ for they shall all know me.
Therefore, based on the previous context, v34 reads “And no longer shall each one [have to] teach his neighbor…[like they did under the law] saying, ‘Know the LORD,’ (But remember none seeks after God, all have gone astray)(like in 1 Chr 28:9 and Jer 22:16-17) for they shall all know me (through the Holy Spirit received in the New Covenant).” In otherwords, under the law, the people are told to seek and know God (which is impossible for a fallen people who hate God, thus they need a savior) but under the New Covenant, it is Jesus Christ our savior who seeks and finds His sheep (This is the same way He saved in the OT too). This New Covenant refers to the New Covenant in which we are truly circumcised in the heart BY GOD Rom 2:25-29 and Col 2:11-14). Since “none seeks after the Lord”, God will choose a people for himself and circumcise their hearts.
So to answer your question “How do Paedo's interpret the prophecy that all people in the NC will "Know the Lord' if infants are in the visible covenant of grace.” I would say the prophecy is not saying EVERYONE in the visible NC will “know God/be saved/have circumcised hearts” but that promise is made to who? “The house of Israel”. God will put the Holy Spirit in the hearts of “ALL the house of Israel” meaning His elect or spiritual Israel. And just like this spiritual Israel are not blood Israel, they also are not the visible mostly Gentile church, but they "are the children of the promise" who are the elect only - these are they that God chose for himself from among the Gentiles as well as blood Jews (see the mystery in Ephesians 3: 6 This mystery is that the Gentiles are fellow heirs, members of the same body, and partakers of the promise in Christ Jesus through the gospel) So the promise is to TRUE spiritual Israel. So within our mostly Gentile churches, they are the invisible elect.
We already know that some adults in the visible church are true Christians and some are not. So I believe the same goes for infants. The adults are baptised into the visible church but only God knows who the invisible elect are who truly belong to spiritual Israel and who have truly been circumcised in the heart. But still some who do not believe are within this visible church and profess to be believers. So I believe the same for children of the New Covenant church also should be baptised into this covenant. Not meaning any offense to dissenters, but I find it odd that adults "allow" other adults to be baptised based on a simple profession of faith (not a very thorough test) but deny children this because "they can't prove their faith?" Well, it's not like the "test"/declaration they made the adults go through was able to weed out the saved adults from the non-believers. Some of these children will grow up and the adults will later come to believe some of these children have already believed at a young age (a gift from God in this New Covenant). But yet they denied the children baptism? How? Because the children couldn't convince the adults they already believed? I struggle with this idea because I cannot remember a day in my life that I did not know God and the idea that I should be "denied baptism" because I couldn't articulate well enough to convince some adult that my faith was real seems unreasonable. My faith was a gift from God! How can an adult tell me "you have to explain and prove to me that you have faith or no baptism?" I was reborn. I didn't know how just like I didn't know where babies came from and how I was born from my mother. Still some children will fall away, proving they were never truly His sheep. But the covenant is from God, the promise is from God and the New life/circumcision of the heart are all gifts from God.
