Infant Baptism--Convince Me - Ask Us Anything

Today Pastor Nathaniel gives a five step argument for infant baptism and five things we should all agree on about baptism, even if we disagree on whether we should administer it to infants.
Here are the five steps to the argument:
1. The church of the Old Testament and the church of the New Testament are, in essence, the same church
2. God includes the children of believers as members of this church
3. In the Old Testament era, children of believers, because they were church members, were given the sign of circumcision
4. In the New Testament era, God has taken the sign of circumcision and changed it to baptism
5. Therefore, in the New Testament era, children of believers, because they are church members, are to be given the sign of baptism.
Here are the five things we should all agree on:
1. Everyone is only baptized once. "Re-baptism" is an oxymoron since there is only "one baptism". Do not get re-baptized and discourage others (including churches) from doing so. 
2. Churches should not require people who were baptized in the Triune name to be re-baptized ads adults in order to be members and take the Lord's Supper.
3. Baptism is primarily God's sign to you, and your reception of it--not your proclamation of faith
4. Baptism is effectual--it is the means by which God gives his salvific grace, even if it is not tied to the moment of administration, and one can still be saved without it.
5. Children of believers are a part of the covenant community, so teach them the faith as disciples (do not see them as pagans to be evangelized).
Other resources: https://opc.org/cce/tracts/WhyInfantBaptism.html#:~:text=God%20has%20initiated%2C%20God%20has,you%20and%20for%20your%20children