Jesus healed the paralyzed man in Luke 5 because He saw "their faith". We don't know if the paralyzed man had faith in Jesus' ability to heal him, but we do know that his friends did. Their faith in Jesus was very evidently manifested in their dogged determination to get their friend to Jesus. In my sermon, I talked about intercessory prayer as an example of how God often blesses others on account of our faith. Here's another important example: infant baptism.
The NT makes it clear that faith in Christ is the prerequisite for baptism (Mk. 16:16; Acts 8:12; 16:31ff.), which is why we don't baptize people unless they profess faith in Christ. We don't get out the fire hose and "baptize" crowds of people because baptism must be received in faith by those who profess their faith in Christ (Rom. 10:9). So why do Presbyterians baptize babies?
The Bible does give some strong indications that even babies can have some form of immature faith/trust (Ps. 22:9; Matt. 18:6; Lk. 1:41), but I'll leave that issue aside for now. The simplest and clearest reason for paedobaptism is this: we baptize the children of believers based on the faith of the parents in the covenant promise of God. Throughout Scripture, God promises to be God to us and to our children (Gen. 17:7; Acts 2:39). Paul even says that children are holy if they have one parent who is a believer (1 Cor. 7:14). These are the promises of God for our children that we are called to trust and embrace, which shapes everything about how we treat children in the church and in our homes (Eph. 6:1-4).
Like the friends of the paralytic who carried Him to Jesus for healing, godly parents are called to bring their babies to Jesus because they believe God's promises (Lk. 18:15-17), and then they are to teach their children to trust God's promises so that their own faith grows and matures. This is the normal pattern of covenant faithfulness that we see in Scripture. The goal of Christian parenting is to pass your faith on to your children, and the most effective way to pass on your faith is to model it by your own joyful obedience.