Exactly! This was a part of first-century Jewish culture, calling for immersion in the
mikveh for new Jewish converts, precisely for this reason. A decent
primer on this states:
"Submerging in a pool of water for the purpose not of using the water’s physical cleansing properties but expressly to symbolize a change-of-soul is a statement at once deeply spiritual and immensely compelling. No other symbolic act can so totally embrace a person as being submerged in water, which must touch and cover every lesion, every strand of hair, every birthmark. No other religious act is so freighted with meaning as this one which touches every aspect of life and proclaims a total commitment to a new idea and a new way of life as it swallows up the old and gives birth to the new.
"The water of the mikveh is designed to ritually cleanse a person from deeds of the past. The convert is considered by Jewish law to be like a newborn child. By spiritually cleansing the convert, the mikveh water prepares him or her to confront God, life, and people with a fresh spirit and new eyes–it washes away the past, leaving only the future. Of course, this does not deny that there were good and beautiful aspects of the past. But, in the strictest religious sense, that past was only prologue to a future life as a Jew."