In most legacy churches, only the trained professional baptizes new believers. There is nothing in the Scriptures to indicate that only a trained professional or a leader can baptize.Can a “layman” baptize a newly converted Christian? Absolutely!
This notion that baptism, like the Lord’s Supper, must be “administered” by a “proper authority” in the church is one of the most perverse holdovers from Roman Catholicism retained by the Reformation. The idea that somehow the benefits and blessing of the Supper and the waters of baptism can only be experienced because someone holding an official ecclesiastical title permits you to has zero, I mean ZERO, basis in the New Covenant church. Under the Old Covenant the case could be made easily but we are not under that old covenant that is obsolete and passing away, we are under the New Covenant, a covenant that is better and not like the Old.
Baptism and the Supper are some of the means God uses to bless His people, not a mechanism He put in place for some in the church to control others.