Romans 8:29 says "For those whom God foreknew he also predestined to be conformed to the likeness of his Son, that he might be the firstborn among many brothers." IOW, as the Nicene Creed explains, he knew us before we knew him. Indeed, he knew us "before all worlds". Or as the 39 Articles says "Predestination to Life is the everlasting purpose of God..."
So the first point I'm making is that salvation is NOT CAUSED BY OR CONFERRED THROUGH BAPTISM, or caused by our decision, but rather salvation is caused by God and conferred through his Holy Spirit. He is the author, period. One cannot force God's hand in this matter, or improve upon his authorship, or deny his authorship, by taking (or not taking) the sacrament.
OK, now let's look at 'sacrament' generally. The point I want to make here is that a sacrament is NOT something that we do but is rather something that God does to signify and seal on earth what He has already done in heaven. In the Eucharist, it is a sign and seal of 'God with us' at the end of all worlds through his crucification and resurrection. In the case of Baptism, it is a sign and seal of His commitment and foreknowledge 'before all worlds' to save a people for himself by remitting their sin.
We might also want to look at the meaning of 'covenant' and why God offers signs of their existence. First, take note that Adam operated under a covenant of works but that after the 'Fall', God offers only a covenant of Grace. Indeed, the mark of Sin on God's creation is precisely the reason for the covenant of Grace, and there is only one; the one Christ makes with his elect.
There are multiple 'covenants' before Christ, of course, but they all point to Him. The covenant with Noah for example (Genesis 9:8-17) says "Never again will the waters become a flood to destroy all life. Whenever the rainbow appears in the clouds, I will see it and remember the everlasting covenant between God and all living creatures." Next we come to the covenant with Abraham (Genesis 12 and 17). Again, it is a covenant of Grace but this time is for Abraham's descendants (through his wife only) and it is signified (and sealed) by circumcision.
If you are still with me, note that the signs/seals given to both Noah and Abraham were NOT given to adult believers only and did NOT confer membership into God's elect. They were rather signs by which God reminded himself of his promises and by which his elect might remind themselves of God's good will toward them.
Now, coming hopefully to a conclusion, I'll point out that Baptism was clearly practiced with children (of believers) in the early church. It is sign and seal of God's good will to all (who believe) as a result of the remission of sin on the Cross.
Let's admit that It is perfectly possible for an adult to be baptized without belief, and that only God can see into the heart and know whether that baptism was 'real' (leading toward salvation). In a similar way, let's also admit that the child of a believer (baptized or not) is supposed to be raised 'in the faith' such that he will eventually appropriate it for himself. As such, it is as reasonable for a child to be baptized by the will of his parents as for an adult to be baptized by the will of himself. In both cases, it does NOT impart, confer or infuse the baptized person with salvation. Instead, it looks to the promise of God to save his Elect; a covenant of Grace, not of works, made by God 'before all worlds' and accomplished in our space and time on the Cross.
Baptism is like a badge or a T-shirt that Christians (and their families) wear to proclaim the remission of sin... and the resulting freedom in Christ. Does God see only the t-shirt? Of course not. He sees to the heart, and not just at a particular moment of a fervent "believer's prayer" or at the water applied to the surface of our skin. He sees our entire life, from our conception to our death. He sees it from the point of view of eternity, not changing his determination as a result of looking at us at some moment of imagined significance in our time line.
Well, that's it. I hope I've made the case for infant baptism.