Institution of Baptism

I was trying to figure out the exact way Baptism was instituted as a Sacrament.
Technically, Baptism was being performed before Christ began His active ministry (and even He was baptised). However, because of St. John the Baptist, is it safe to say that Baptism was instituted by Christ, through the person of St. John the Baptist?
And any other ideas/perspectives are welcome…

"Now the eleven disciples went to Galilee, to the mountain to which Jesus had directed them. … And Jesus came and said to them, “All authority in heaven and on earth has been given to me. Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, and teaching them to obey everything that I have commanded you. …”.
(Matthew 28:16-20. New Revised Standard Version)

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