"Perhaps the greatest evidence that Jesus did exist is the fact that literally thousands of Christians in the first century A.D., including the twelve apostles, were willing to give their lives as martyrs for Jesus Christ. People will die for what they believe to be true, but no one will die for what they know to be a lie". -Excerpt from http://www.gotquestions.org/did-Jesus-exist.html
Detailed accounts of how the apostles were tortured & killed can be found in "Foxe's Book of Martyrs". Peter's cruel, torturous death was one where he suffered immensely. Peter's faith in Jesus has been the one that has been the greatest inspiration to me. Peter, the apostle who so easily denied knowing Jesus 3 times when Jesus was still alive.......refused to deny Jesus after Jesus' "death", even when it cost him his own life in a very cruel & torturous way. Peter suffered immensely as he was killed and all he had to do was deny Him "one more time" but Peter refused because he "believed". People just don't go around subjecting themselves to that kind of pain & torture unless they believe they KNOW "the truth".
I've read the "Foxe's book of Martyrs", and know what you speak of. Many Christians gave their life for their belief in Christ, and that is a witness of divine love and strong witness to their Faith. Many Christians were tormented and killed in the Roman Collosium for sport. I believe there is a Martyrs crown laid up for all those who give their life in the service of God receive.
However, there are many religions where they are laying down their lives for their God. The Muslim Allah comes to mind. These people are so brain washed that they believe that martyr in the name of Allah, grants them paradise immediately with virgins or whatever. While their at it, taking a few infidels with them is glorious...or so they are taught.
After the rapture, the plan of Salvation no longer applies, as the Spirit of God that "strived" with man, is gone. Everyone who has the Spirit of God in them is gone also. So how do people get saved during that time? The Bible talks of those being martyred that would not take the mark of the beast.
I think the only proof we can offer is to live our lives in accordance with the Word. We are the only Bible that some people will ever read. To be separated from the world and live for Jesus that died for us. It's our own personal testimony that will either declare His existence. It's Christ in us, the hope of glory. If we have passed from death unto life, a change will happen in our life. If we live Holy and separated from the world, the world will take notice that we are different. Many people that I knew before I knew Christ, are now saved because of the change in my life after my conversion. Not me, but the God that lives in me, that does the work, as I yield and submit to His Word. If we claim to know God, but live the same as we did before we were converted, then our witness is in vain.
We are demanded time and again to prove that God exists. We are the living epistles known and read of all men. As far as I know, that's the only "proof" God will give this generation. We can no more explain Faith, than how the bones of a child are knit in the womb of the mother. I've witnessed the infilling of the Holy Ghost with the evidence of speaking in other tongues. That is about as supernatural on this earth as you can get. Do people believe it? No. It's explained away with whatever. Thing is, I have it, and nobody can tell me that it's not real, and/or it's not God....I know better. The inner workings of the Spiritual Gifts that are associated with the same Spirit cannot be explained unless you have the Spirit of God to "quicken" them to you.
What I'm saying is they wanted a "sign" of proof in Jesus time also. Jesus went around healing, teaching, etc., and it got Him death on a cross from the religious leaders of that time. We ourselves need to be living testimonies of the existence of God.