Neither the apostles nor first Christians could have understood that Christ commanded them to baptize with water nor that he prescribed any formula therefor, otherwise they would have used this formula and have referred to this command as authority for their subsequent water baptism.  But so far as Scripture informs, no one in those early days ever did baptize with water in the name of “The Father, Son and Holy Spirit,” nor ever heard of such formula.

Sometimes they baptized in the name Jesus, Lord or Christ, but never one word about the Father nor the Holy Spirit.[34]

Some baptized without formula, or if they did use formula it was not considered of sufficient importance to mention.[35]

They baptized with water before Christ gave them their commission, and continued to baptize in the same way after, which is another proof that their authority for water baptism did not originate in Christ’s command.[36] Nearly thirty years after Christ, some believers who were fervent in Spirit and instructed in the ways of the Lord, continued to baptize with John’s baptism and we don’t know how much longer it continued.[37]

When was Christ’s command first quoted as authority for water baptism?

Not in apostolic times, not until long after.

When did man first presume to baptize with water, in the name of the
Father, Son and Holy Spirit?

Some of our oldest writings[38] indicate the use of this formula in some places, probably in the early part or middle of the second century.  Yet, Schaff, who was familiar with all these old records, says this formula is not traceable in its present shape earlier than the fourth century.

Evidently the apostles and first Christians continued to baptize with water, because it was a conspicuous feature in the special mission of John the Baptist as well as a Jewish rite in which they and their fathers were educated.  They had no thought of Christ’s command as authority for water baptism.

Paul said plainly that he had no such authority.  Christ sent him not to baptize but to preach the Gospel.[39]

Paul thanked God that he had baptized so few.[40] He could not have spoken thus slightly of Christian baptism.  It must have dawned upon him that in the fulness of the Christian dispensation there was no place for water baptism; otherwise how could he thank God that he had baptized so few?  What dispenser of water baptism could give such thanks in this day?  Paul circumcised Timothy, and perhaps Titus, because of the Jews.  Did he not baptize those few with water for the same pacific purpose, or did he not at first receive full light upon this subject?[41]

Some assume that Christ gave others authority to baptize which did not extend to Paul.

We cannot believe that all Christ’s ministers to the end of the world were commissioned to baptize with water, Paul only rejected.[42] This reflects unjustly upon Paul, the great apostle to us Gentiles.[43] Is it not a mere evasion of the gospel truth here and elsewhere inculcated, that Christ gave no commission to baptize with water?[44]