Technically, babies are already in the covenant before they are baptized. We see this clearly in the Old Covenant when the babies who are not circumcised on the right day are to be cut off from his people because they have broken the covenant (Gen. 17:14). You can only break the covenant if you are in it. Also, we see this in 1 Cor. 7 when Paul tells us that the children of believers are holy (1 Cor. 7:14.
We baptize them in faith, trusting that the promises of God to us and to our children will be fulfilled and that our children will walk with God and will bring their children up in the nurture and admonition of the Lord. We do not presume on God’s promises. God works through means to accomplish his goals. He wants godly offspring (Mal. 2:15) and that is what we want too. So we raise our children in faith and trust in a faithful God.
The Covenant of God is not one we look back on as much as one we live in. Christianity is about living Coram Deo—in front of the face of God. We look back to gain examples of others who have gone before us and we look forward to hope for what God has in store for us, and we live in the present in the light of those two other vantage points.
This covenant is the same covenant that God made with Adam, Noah, Abraham, David, etc. It is just fulfilled in Christ. They aren’t new covenants each time, they are the same covenant renewed. Even the New Covenant is not a different covenant, it is the Old Covenant, died and resurrected. It was always to be the way it is now. It is Eden restored in a sense (that sin thing gets in there and makes it harder to see).
Another way to look at it is that God created Adam and Eve to start his kingdom on earth. They sinned and caused a mess. Jesus came, cleaned up the mess, and restored the coming of the Kingdom of God on the earth. So, we are not waiting for the kingdom to come, we are part of the Kingdom coming. We are not waiting for it to start, we are waiting for it to be completed. We are part of the Kingdom of God, the people of God, a kingdom of priests, a holy nation, a resurrected man, the church, the body of Christ, etc.