Acts 8:
36 Now as they went down the road, they came to some water. And the eunuch said, “See, here is water. What hinders me from being baptized?”
37 Then Philip said, “If you believe with all your heart, you may.”
And he answered and said, “I believe that Jesus Christ is the Son of God.”
38 So he commanded the chariot to stand still. And both Philip and the eunuch went down
into the water, and he baptized him.
It's worth noting that verse 37 is generally agreed to be a late addition to the text, and also should be understood in the context the historic Christian practice of the Rite of Baptism. Namely adult converts were expected to go through a process of catechesis, such persons were known as catechumens; and at Baptism they would be asked, "Do you believe..." and they would answer in the affirmative. It's still how the majority of Christians practice the Rite of Baptism today. And these baptismal creedal formulas are the foundation of all the historical Creeds of the Church. It's why we see the proto-creeds, such as those by St. Irenaeus, split into three parts, also why the Old Roman Symbol (the basis for the Apostles' Creed) and the Nicene Creed have a three-part structure:
Belief in God the Father the maker of all things.
Belief in Jesus Christ, the Son of God, our Lord, who was born of the Virgin Mary, suffered under Pilate, was crucified, dead, buried, and rose again.
Belief in the Holy Spirit, the Christian Church, the resurrection of the dead, and the life everlasting.
Why three parts? Because Christian baptismal practice was three-fold. Standard procedure was three-fold immersion in the name of the Father, Son, and the Holy Spirit. Or, barring a sufficient quantity of water for immersion, three-fold affusion (aka pouring) in the name of the Father, Son, and the Holy Spirit.
So the context of this particular statement is likely borne out of the Church's own historical procedure. What this passage doesn't do is what some try and make it do, and that is to deny Baptism to young children. Because the ancient and universal practice of the Christian Church has always been to administer baptism to the children of believers. And so entire families, indeed entire households, would be baptized (just as we see in the Acts of the Apostles), not just the adult converts but also their children; and also children born to believing parents would in the same way be baptized. This is clearly evidenced by everything we read about in the earliest days of Christianity.
This makes sense, because this is exactly how conversion to Judaism worked. A convert to Judaism would, among other things, go through a ritual washing in the mikveh, this is the precursor to Christian Baptism. And two thousand years ago, just as today, when parents converted, their children would also be converted, this meant circumcision for sons, and ritual washing in the mikveh for everyone. Without the mikveh washing the conversion was not accomplished. And so, quite naturally, early Christians took it for granted that conversion to Christianity, through Baptism, wasn't limited to adults, but was for entire families. It's why, again, we read that entire households were baptized. Because this was normal, it simply wouldn't have occurred to the Apostles or any of the early Christians to do it any differently.
The difference between the use of the mikveh in conversion to Judaism and Christian Baptism is that Christian Baptism receives its authority from Jesus Christ, as part of His command for His Church to make disciples and baptize them, and that this is done in the name of the Father, Son, and the Holy Spirit. But the language surrounding Christian Baptism still carried over from the use of the mikveh for conversion, for example the language of new birth. Which is why Jesus speaks of the new birth as being of "water and the Spirit", and questions Nicodemus asking, "How are you a rabbi in Israel and yet you don't know this?" Nicodemus, a rabbi, a teacher, an instructor on Jewish law and practice, would have known that when a Gentile undergoes the washing during conversion that it brought about a kind of new birth, being born afresh as a child of God's covenant. There is an intentional link between Jewish conversion practice and the institution of Christian Baptism; in the same way that there is an intentional link between the Jewish Passover and the Lord's Supper.
So "If you believe" in Acts 8:37 isn't about gatekeeping, but about the association of faith with Baptism. Which has always existed in Christian practice. Young children--including infants--are baptized and raised in the faith, and their faith matures as they are nurtured by the Church; in the same way that an adult convert is baptized, and their faith is also nurtured by the Church. Faith comes by hearing, and hearing by the word of Christ says the Apostles (Romans 10:17), and whether that involves being baptized as a baby and being raised in the faith or converting as an adult and receiving Baptism as an adult convert, it is the same Word, the same Faith, and indeed the same Jesus Christ who brings us into His Body and makes us members and partakers of Himself through His Word and Sacraments.
-CryptoLutheran