You are making a leap of logic that isn't warranted. Scripture does not say that one MUST HIMSELF believe before being baptized. I am not aware of a Scripture verse that says "a person can't be baptized unless THAT person believes". You are presuming that because baptism is ordinarily described as a ritual that believers go through to enter union with the Spirit, you think that believers ONLY can be baptized. I don't find that anywhere in Scriptures. The Scripture says that entire households were baptized. It is very likely that would include infants, as most families of the day had many children. Therefore, infant baptism is NOT invalid.
Regards
Mark 16:16
He that believeth and is baptized shall be saved; but he that believeth not shall be damned.
According to Christ, who needs to believe in order for one to be saved?