In God's soverignty, He decided on His own, without counsel from man, that He would save those who believe (1 Cor 1:21) the seemingly foolish gospel that Jesus died on the cross for our sins. He gave the ability to believe to everyone, and He saves everyone who believes. The logic that says He pre-determined everyone's choice to believe (or not to believe) and the companion logic that it is only possible to believe if God flips a switch are both very difficult to reconcile with the pany (perhaps hundreds) of verses that ask people to put their trust in Christ. And thinking that God would broadcast to all the world's hungry, blind, naked, and poor people a message of hope, only to hold it out of reach from most people is unimaginable to me. So yes, I believe God offers salvation in Christ to everyone and leaves it up to each one of them to choose. But of course, faith has never saved anyone. Only Jesus can save people, and He saves everyone who believes.