Ambrose was the Bishop of Milan, a canonized saint and a doctor of the Church. His own words clearly demonstrate that he believed in the sacraments as taught by the Catholic Church, so I don't know how anyone can argue he thinks we are saved by faith alone.
He clearly believes in baptismal regeneration and in the sacrifice of the Mass and the Real Presence.
Ambrose of Milan"We saw the prince of priests coming to us, we saw and heard him offering his blood for us. We follow, inasmuch as we are able, being priests, and we offer the sacrifice on behalf of the people. Even if we are of but little merit, still, in the sacrifice, we are honorable. Even if Christ is not now seen as the one who offers the sacrifice, nevertheless it is he himself that is offered in sacrifice here on Earth when the body of Christ is offered. Indeed, to offer himself he is made visible in us, he whose word makes holy the sacrifice that is offered" (
Commentaries on Twelve Psalms of David 38:25 [A.D. 389]).
On the Mysteries, by Ambrose:
Chapter 6
32. Peter was clean, but he must wash his feet, for he had
sin by succession from the first man, when the serpent overthrew him and persuaded him to
sin. His feet were therefore washed, that hereditary
sins might be done away, for our own
sins are remitted through
baptism.
Chapter 7
34. After this white robes were given to you as a sign that you were putting off the covering of
sins, and putting on the chaste veil of innocence, of which the
prophet said: You shall sprinkle me with
hyssop and I shall be cleansed, You shall wash me and I shall be made whiter than snow. For he who is
baptized is seen to be purified both according to the Law and according to the
Gospel: according to the Law, because
Moses sprinkled the blood of the lamb with a bunch of
hyssop;
Exodus 12:22according to the
Gospel, because Christ's garments were white as snow, when in the
Gospel He showed forth the
glory of His Resurrection. He, then, whose guilt is remitted is made whiter than snow. So that God said by Isaiah: Though your
sins be as scarlet, I will make them white as snow.
Isaiah 1:18Chapter 8
47. We have
proved the
sacraments of the
Church to be the more ancient, now recognize that they are superior. In very
truth it is a marvellous thing that God rained
manna on the fathers, and fed them with daily food from heaven; so that it is said, So man ate
angels' food. But yet all those who ate that food died in the wilderness, but that food which you receive, that living Bread which came down from heaven, furnishes the substance of
eternal life; and whosoever shall eat of this Bread shall never die, and it is the Body of
Christ.
48. Now consider whether the bread of
angels be more excellent or the Flesh of
Christ, which is indeed the body of life. That
manna came from heaven, this is above the heavens; that was of heaven, this is of the Lord of the heavens; that was liable to corruption, if kept a second day, this is far from all corruption, for whosoever shall taste it holily shall not be able to feel corruption. For them water flowed from the rock, for you Blood flowed from Christ; water satisfied them for a time, the Blood satiates you for
eternity. The Jew drinks and thirsts again, you after drinking will be beyond the power of thirsting; that was in a shadow, this is in
truth.
49. If that which you so wonder at is but shadow, how great must that be whose very shadow you wonder at. See now what happened in the case of the fathers was shadow: They drank, it is said, of that Rock that followed them, and that Rock was Christ. But with many of them God was not well pleased, for they were overthrown in the wilderness. Now these things were done in a figure concerning us.
1 Corinthians 10:4 You recognize now which are the more excellent, for light is better than shadow,
truth than a figure, the Body of its Giver than the
manna from heaven.
Chapter 9
The whole thing is Ambrose explaining how the Eucharist is the Real Presence and how Christ is actually present at baptism and effecting a real, sacramental regeneration.