This question has been answered many times before and in many ways so this is just a brief comment. The Lutheran Church baptizes at any age meaning that age is not the focus of or the requirement for baptism. Scripture nowhere mandates an age for baptism. It is how we understand baptism that gives us an understanding why baptizing infants is a good practice.
First, it is given by divine revelation. In addition, the practice is followed by the one, holy, catholic, and apostolic Church, from the earliest of times. Lutherans do not view baptism as symbolic or as a work of man but as a gift of God and His mercy. For children born in sin there is no greater gift than God's mercy and forgiveness. Also, God puts His holy Name on them and makes them His children. The water combined with God's Word brings God's Spirit to us in baptism. Being baptized means putting on Christ and being clothed with Him and His righteousness. In baptism we are buried with Christ into His death and raised with Him in His resurrection to new life. We can call it a gift of God's Spirit, a gift of His grace, a means of grace, a sacrament. Those who are connected to God in Christ are rescued from death and the devil. They are given the forgiveness of sins. Or as the Apostle writes in his letter to Titus, "He saved us through the washing of rebirth and renewal by the Holy Spirit, whom He poured out on us generously through Jesus Christ our Savior, so that, having been justified by His grace, we might become heirs having the hope of eternal life."
There is no greater gift to give to helpless infants, our own children. Also, this gift is not limited to the few minutes it takes to baptize but it is a gift with a promise to eternal life. Baptism is not dependent on our age but on God's grace and mercy. Baptism is a focus on Christ and His salvation poured out on us. Baptism is not a work of men but a gift from God that the Church freely shares as she has graciously received from the Lord.