I personally believe that Christians originally did not have to be baptised to follow Christ. They simply had to be Jews and profess faith in Jesus. Christianity after all was just one of many Jewish sects attending Temple and Synagogues.
When the Sanhedran eventually ruled that the sect were heretics (because so many adult Gentiles were joining and not fully following Jewish practises like circumcision and dietary practises) then Christians simply kept using the old Jewish Mikveh with a Trinitarian formula as the rite of passage for joining adults.
As the sect had so many ex followers of John the Baptists sect this was entirely natural. It also gained the extra theology of a Divine forgiveness of all sin accordingly.
Infant baptism was not originally an issue because most converts early on seem to be adults. However as babies were born increasingly to Catholic parents, who were now considered sinful due to Baptist theology (unlike Judaism?) an early Mikveh was eventually necessitated and replaced the infant circumcision/presentation ceremonies no longer practised with Gentile Christians even when formerly a Jewish sect.