Even in the very first part of that speech, St. Ambrose confirms that BOD was actually not a Catholic doctrine taught everywhere in the early Church as the BODers falsely pretend. He says to his audience: "
but I hear you grieve because he did not receive the Sacrament of Baptism"... Now...why would they grieve about this? the answer is obvious: because they firmly believed, as they had been correctly taught, that catechumens are still not part of the Church and that to enter Heaven is necessary to receive the water Baptism. They grieved because they knew that Valentinian was oriented to Hell if dying in such an unbaptized state given that
such was the Catholic doctrine taught everywhere since Our Lord walked the earth. In other words, their grief was because they took the words of Jesus Christ in John 3:5
literally, as it is the correct position of the Church.
And after all this misunderstanding, we have St. Ambrose undoubtedly defending the necessity of water Baptism for salvation, even for catechumens, as one of the Fathers who were more vehement about it. In
The Mysteriies he says:
One is the Baptism the Church administers: the Baptism of water and the Holy Ghost...with which catechumens need to be baptized...Nor, again, is there the Sacrament of Regeneration without water: “For except a man be born again of water and of the Spirit, he cannot enter into the kingdom of God.” John 3:5 Now, even the catechumen believes in the cross of the Lord Jesus, wherewith he too is signed; but unless he be baptized in the Name of the Father, and of the Son, and of the Holy Spirit, he cannot receive remission of sins nor gain the gift of spiritual grace.