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There is physical baptism with water, but here Paul seems to speak of spiritual baptism with the Spirit of God. It is that baptism that made us God’s children through faith and causes us to “put on” Christ. To put on Christ would be to put on his character, Christlikeness.
And we pray:
We are Your children, O Lord, for You have made us such. By faith, You adopted us; by The Spirit, You sanctified us to Yourself. As physical children resemble their parents, so make us also to resemble You, being Your spiritual children. Let us strive today to live in a way that lets all see that we are the children of God indeed. Amen.