From this mystery of unity it follows that all men and women who are saved share, though differently, in the same mystery of salvation in Jesus Christ through his Spirit. Christians know this through their faith, while others remain unaware that Jesus Christ is the source of their salvation. The mystery of salvation reaches out to them, in a way known to God, through the invisible action of the Spirit of Christ. Concretely, it will be in the sincere practice of what is good in their own religious traditions and by following the dictates of their conscience that the members of other religions respond positively to God's invitation and receive salvation in Jesus Christ, even while they do not recognize or acknowledge him as their saviour (cf. AG 3,9,11).
DIALOGUE AND PROCLAMATION: (vatican.va)
I don't believe this is saying what you believe it is saying.
I understand what it sounds like - that no one needs to have faith in the Lord Jesus Christ to receive salvation - they do not need to recognize or acknowledge Him at all to receive salvation.
Let me quote a later portion of this same reflection,
"
35. Religious traditions and the Church
To the Church, as the sacrament in which the Kingdom of God is present "in mystery", are related or oriented (
ordinantur) (cf. LG 16) the members of other religious traditions who, inasmuch as they respond to God's calling as perceived by their conscience, are saved in Jesus Christ and thus already share in some way in the reality which is signified by the Kingdom. The Church's mission is to foster "the Kingdom of our Lord and his Christ" (
Rv 11:15), at whose service she is placed. Part of her role consists in recognizing that the inchoate reality of this Kingdom can be found also beyond the confines of the Church, for example in the hearts of the followers of other religious traditions, insofar as they live evangelical values and are open to the action of the Spirit. It must be remembered nevertheless that this is indeed an inchoate reality, which needs to find completion through being related to the Kingdom of Christ already present in the Church yet realized fully only in the world to come."
So - in summary - the Catholic Church recognizes that God is working throughout the world through the ministrations of the Holy Spirit - not just in the Catholic Church.
Even though the "inchoate reality" - meaning "not fully formed or completed" reality - of God's Kingdom does exist on Earth - it only finds "completion" through "being related to the Kingdom of Christ already present in the Church" and is only fully realized "in the world to come".
Meaning - those who do not accept the Lord Jesus Christ during mortality on Earth can only find salvation - entrance into God's Kingdom - after they have become "related" to the Kingdom of Christ - which will be fully realized in the world to come.
It is basically as Paul said in his epistle to the saints in Philippi,
"Wherefore God also hath highly exalted him, and given him a name which is above every name:
That at the name of Jesus every knee should bow, of things in heaven, and things in earth, and things under the earth;
And that every tongue should confess that Jesus Christ is Lord, to the glory of God the Father." (Philippians 2:9-11)
No one receives salvation until they bow and confess that Jesus Christ is the Lord.
So - according to the Catholic Church - all Mankind can be saved -
if they accept this "invitation" from God.
They will "respond positively" to this "invitation" if they are "sincere" and "practice of what is good in their own religious traditions and by following the dictates of their conscience".
If they have done this - which is following the Holy Spirit - they "already share in some way in the reality which is signified by the Kingdom".
However - this reality is "inchoate" - and they can only find a "completion" by "being related to the Kingdom of Christ already present in the Church" and is only fully realized "in the world to come".
This "full realization" comes after they accept God's "invitation" which to bow down and confess that Jesus Christ is the Lord - then they receive salvation.
It is better to accept and have faith in the Lord Jesus Christ in this life - but all of Mankind will be required to do so in the next - and if they were sincere in this life they will accept this "invitation" of God.
The Catholic Church teaches that all Mankind needs to accept and have faith in the Lord Jesus Christ in order to receive salvation.
It is better to do so in this life - but the sincere can do so in the next life - but it is a requirement nonetheless.