I assume nothing.
Acts 8:36 And as they went on their way, they came unto a certain water: and the eunuch said, See, here is water; what doth hinder me to be baptized?
37 And Philip said, If thou believest with all thine heart, thou mayest. And he answered and said, I believe that Jesus Christ is the Son of God.
38 And he commanded the chariot to stand still: and they went down both into the water, both Philip and the eunuch; and he baptized him.
Yes, you assume.
One case from scripture or even several does not change the fact that early Christians used baptism on infants without any expectation of faith at that moment on the baby's part.
Again, 8 day old Jewish babies did not get to wait until they were old enough to believe in, or choose on their own, the covenant before being circumcision.