It is your premise that the hearts and souls of a vast majority are doomed. Quite frankly, Christ never commanded His followers to judge the eternal fate of others. He commanded the Gospel be preached with Him as Lord and Savior. What we do know from Acts 17 is that those who hear have no excuse:
Acts 17:
22 Then Paul stood in the midst of the Areopagus and said, “Men of Athens, I perceive that in all things you are very religious; 23 for as I was passing through and considering the objects of your worship, I even found an altar with this inscription:
TO THE UNKNOWN GOD.
Therefore, the One whom you worship without knowing, Him I proclaim to you: 24 “God, who made the world and everything in it, since He is Lord of heaven and earth, does not dwell in temples made with hands. 25 Nor is He worshiped with men’s hands, as though He needed anything, since He gives to all life, breath, and all things. 26 And He has made from one blood every nation of men to dwell on all the face of the earth, and has determined their preappointed times and the boundaries of their dwellings, 27 so that they should seek the Lord, in the hope that they might grope for Him and find Him, though He is not far from each one of us; 28 for in Him we live and move and have our being, as also some of your own poets have said, ‘For we are also His offspring.’ 29 Therefore, since we are the offspring of God, we ought not to think that the Divine Nature is like gold or silver or stone, something shaped by art and man’s devising. 30 Truly, these times of ignorance God overlooked, but now commands all men everywhere to repent, 31 because He has appointed a day on which He will judge the world in righteousness by the Man whom He has ordained. He has given assurance of this to all by raising Him from the dead.”
32 And when they heard of the resurrection of the dead, some mocked, while others said, “We will hear you again on this matter.” 33 So Paul departed from among them. 34 However, some men joined him and believed, among them Dionysius the Areopagite, a woman named Damaris, and others with them.
Isn't that what the Bible says, that few will find the Gate?