Where does the text say "there was belief" in this sequence of events? It doesn't. (You quoted 11:17, but "the same gift as He gave to us also after believing in the Lord Jesus Christ" is talking about Peter and the Apostles at Pentecost, not Cornelius. This is clear enough on a close reading of the translation you used; the 1978 NIV is more explicit about referencing the "us" here to Peter and the Apostles: "So if God gave them the save gift as he gave us, who believed in the Lord Jesus Christ. . .") 10:34f quotes Peter's sermon up to verse 43; then in 44 it says that while Peter was talking, the Holy Spirit fell upon Peter's hearers. The key salvific event here is the Holy Spirit coming upon them, which Peter identifies as the baptism of the Holy Spirit in 11:16. "Baptism" does not reduce to water--this is the point I was trying to make. Baptism is most fundamentally a union of the individual Christian with Christ through the Holy Spirit--see Romans 6 again on this. This normally happens at the same time as water baptism, which is why the NT sometimes speaks of baptism or the water of baptism "saving". Cornelius' case simply illustrates that water and Spirit baptism do not necessarily occur at the same time in certain extraordinary cases. But the normal sequence is that illustrated by Jesus' own baptism: water baptism first, then the Spirit descends for spiritual baptism. Jesus' baptism is the role model held up to Christians by Paul, not Cornelius'.
I agree with you (and the Catholic Church agrees) that baptism without repentance and faith is only getting wet. The point I am also making, though, is that repentance and faith are only salvific because of the more central role the Holy Spirit--that is, God Himself in the Third Person of the Trinity--plays in baptism. My human efforts at faith and repentance cannot save me without God's grace, which is poured out by and in the Holy Spirit.
And you are right that genuine faith must bear fruit. However, Luther did introduce a doctrine called Sola fide which some people have taken in that direction, which is why I was refuting that.
Regarding Titus 3:5, I quoted what Paul wrote--how is that taking anything out of context? If you had read the link on baptism of desire I included in my post, you would have seen that it already answers your question about whether a person dying after a car wreck can be saved without water baptism. It sounds like you didn't hear the point I was making on baptism being fundamentally an action of the Holy Spirit. I was not suggesting, and the NT does not teach, that water alone is the salvific agent in baptism. I think we might actually agree on some of that but we are not using the same terminology.
You did not post the entire verse. I'm not a fan of cutting out part of the verse.
He tells Titus, "He saved us through the washing of rebirth and renewal by the Holy Spirit" (Titus 3:5).
The verse needs to be understood in the context of the passage.
The passage, in context, points towards faith in Him is what saves as noted in 3:7. It is not on the basis of deeds as noted in 3:5.
I agree with you (and the Catholic Church agrees) that baptism without repentance and faith is only getting wet. The point I am also making, though, is that repentance and faith are only salvific because of the more central role the Holy Spirit--that is, God Himself in the Third Person of the Trinity--plays in baptism. My human efforts at faith and repentance cannot save me without God's grace, which is poured out by and in the Holy Spirit.
On this I agree.
And you are right that genuine faith must bear fruit. However, Luther did introduce a doctrine called Sola fide which some people have taken in that direction, which is why I was refuting that.
My understanding has always been that no matter how "good" we are or how many "good deeds" we do those are of no avail without faith in Christ first. I think the point Luther was trying to make is that even those deeds do not save us. They are evidence of our salvation. Ephesians 2:8-9 makes this clear: For by grace you have been saved through faith; and not that of yourselves, it is the gift of God, not as a result of works so that none may boast.
It sounds like you didn't hear the point I was making on baptism being fundamentally an action of the Holy Spirit. I was not suggesting, and the NT does not teach, that water alone is the salvific agent in baptism. I think we might actually agree on some of that but we are not using the same terminology.
I agree the Holy Spirit moves one to salvation.
The normal order of how one comes to Christ:
Hear or read the Gospel message.
Believe the message...not just intellectualize it.
The Holy Spirit falls/enters/comes upon the person.
Baptism.
Fruit is produced.
You may be right....we may be closer on this that we realize.