For the first century and a half of Christianity, the rite of baptism was performed using living water. That was not just because of the poverty of the early Christians, but also because of their understanding of the text in KJV Jeremiah 2: 12-13 (NC 1:5) and also 17:13 (NC 7:1).
The earliest depictions of baptism in early Christian art were invariably in a lake, stream or river. The iconography of the early Christians depicting living water ended in about the fourth century, but a lot of things changed around that time also.
The early text of instructions known as The Didache is believed to have been written in the first century. In Chapter 7, verse 2, it instructs to perform baptism in this way: “Concerning baptism, baptize thus: Having first rehearsed all these things, ‘baptize, in the Name of the Father and of the Son and of the Holy Ghost,’ in running water[.]”
Both Matthew and Mark clarify that John the Baptist performed baptism, including of Jesus Christ, in the River Jordan. (NC Matt. 2:3-4; Mark 1:1-2.)