With God nothing is impossible.
However, we know He will not eternally reward sin. Is it possible for Him to do so? It is utterly repugnant to even answer this in any other way than NO! I will not ever say it is possible for God to reward sin, because this is a travesty against His justice, which is perfect.
Now, to suggest that He would act in a manner contrary to His justice in any other manner is equally repugnant. Christ Himself said that certain types of people cannot enter heaven: The unbaptized. Those are the clear words out of His own mouth.
The Holy Catholic Church, established by Jesus Christ is given the "promise of the Father", that "power from on high", by which She might "religiously guard and faithfully expound the revelation or deposit of faith transmitted by the apostles," the promise who is none other than "the Spirit of truth", who is come to "teach you all truth", has wielded this very great power on not few occasions, whereby She infallibly proclaims the absolute and true meaning of the words of Jesus Christ in St. John 3:5.
One such definition is this:
Holy baptism holds the first place among all the sacraments, for it is the gate of the spiritual life; through it we become members of Christ and of the body of the church. Since death came into the world through one person, unless we are born again of water and the spirit, we cannot, as Truth says, enter the kingdom of heaven.
The sacrament of water baptism is described as the means of entering the Church, and is directly referenced as the meaning of being born again of water and the Spirit, and it is then further asserted that indeed as the Truth Himself says, we cannot, enter the kingdom of heaven unless we partake in this being born again of water and the spirit - and there is not an exception given. It is impossible, insomuch as God said HE wouldn't allow it, regardless of His omnipotence. His omnipotence does not mean that we can speculate that He will transgress His JUSTICE, for the sake of a person who "dies before their time" as though God's providence somehow could not foresee it, or as though He did not have the ability to prevent such a death, or to reverse it for the sake of getting his elect the baptism, without which, according to His own words, one is damned.
That was indeed God the Holy Ghost who spoke through Pope Eugene, giving testimony of and confirming the Truth of the Lord Jesus Christ's words. And you have seen enough times that the Vatican Council and Pope Pius X, who you all claim to obey, both teach that the meaning is to be held that was once declared by Holy Mother Church, and Pope Leo XIII, who you all claim to obey, stated that if anyone recedes in the LEAST from even ONE point of doctrine proposed by the Church's authoritative Magisterium (such as that of Pope Eugene), he is NOT A CATHOLIC.