No they don’t. Baptism of children follows inline with the state of birth which is necessary for the Salvation of the Soul wherefore the fall took place. Thus, which we know that Christ was a male babe born through a woman, “born under the law.” From which a divine hotspring of a miracle through the Announcement of an Angel, Gabriel. Now, if you dispute, science does not/cannot. Two indicators (science wise the miracle virgin birth): A.) The Big Bang Theory shows even with miniscule particles expanded into the Universe and all things created, which still holds place in the account of Genesis. B.) We know that from hertz/frequency ranges in bandwidth with no visible characteristic can be heard and scene through receptive instruments. You say nature cannot do this process without man? Sure, the Angel provided by the Creator, did. Thus, science cannot dispute the things she employs as well. Which means the state of the Priesthood follows inline with the state of one's birth/origin.