I would agree that it is God's desire that His word would go out to the entire world. Some people (His Elect) will hear His word and come to faith. For others, their heart will be hardened and they will be left without excuse. It was never God's plan to save the entire world. If that were His plan, then the entire world would be saved.
To those who think that we must first believe (a work on our part) before being saved, please consider the following teaching.
For these views contradict the Holy Scriptures, which testify that God does infuse or pour into our hearts the new qualities of faith, obedience, and the experiencing of his love: I will put my law in their minds, and write it on their hearts (Jer. 31:33); I will pour water on the thirsty land, and streams on the dry ground; I will pour out my Spirit on your offspring (Isa. 44:3); The love of God has been poured out in our hearts by the Holy Spirit, who has been given to us (Rom. 5:5). They also conflict with the continuous practice of the Church, which prays with the prophet: Convert me, Lord, and I shall be converted (Jer. 31:18).