John 10:22-30 NASB
At that time the Feast of the Dedication took place at Jerusalem; it was winter, and Jesus was walking in the temple in the portico of Solomon.The Jews then gathered around Him, and were saying to Him, "How long will You keep us in suspense? If You are the Christ, tell us plainly." Jesus answered them, "I told you, and you do not believe; the works that I do in My Father's name, these testify of Me. But you do not believe because you are not of My sheep. My sheep hear My voice, and I know them, and they follow Me; and I give eternal life to them, and they will never perish; and no one will snatch them out of My hand. My Father, who has given them to Me, is greater than all; and no one is able to snatch them out of the Father's hand. I and the Father are one."
We see here that Jesus specifically says that the reason why the Pharisees didn't believe was because they weren't His sheep, not the other way around. He also says that He gives eternal life to His sheep, not that they will be His sheep when they receive it. If He is giving it to His sheep, they must have not had it before while still being His.
There is no examples outside the fact that God chose those who will believe, thus receiving salvation. Jesus also said many are called but few are chosen. A general call of repentance may be for all, but only the few who take the offer (for whom it was purposed for) will be the ones who are chosen will believe.
Jesus is the only way to be saved.