"for we walk by faith, not by sight" (ASV)
I can't count how many times I have been asked to prove that what the Bible says is true. The truth of the matter is that I have absolutely no proof that an unbeliever will be willing to accept. My proof is through my experiences, which are largely indemonstrable, and through my faith, which is foreign to someone who does not believe in God.
Often Christians find themselves shaken at the lack of evidence of God's existence. In our society, in order to believe something to be real, most people need to see proof. When they realize they can't produce any that someone else would accept, some Christians start to doubt.
This is yet another problem of perspective. When we doubt because of a lack of "evidence" are looking at things from an earthly perspective. The truth is, there is no concrete evidence to be seen that would satisfy those who doubt. Even those who were face to face with Jesus and witnessed His miracles often didn't believe. How then should we hope to convince a generation who has not seen tangible evidence?
"Now faith is assurance of things hoped for, a conviction of things not seen." (Hebrews 11:1 ASV) Until Christ's return, we as Christians are called to believe not by proof, but by faith. Hebrews 11 goes on to give account of many times when faith has served the men and women of the Old Testament who followed God's commands. Likewise, faith still has power today. If we walk by faith, following God's lead though we have no proof that it will work out well in the end, we will see all the blessings that God has in store for us.
Christ knew the difficulty of belief without proof. After he rose from the dead, when confronted with Thomas' doubts, "Jesus saith unto him, Because thou hast seen me, thou hast believed: blessed are they that have not seen, and yet have believed." (John 20:29 ASV) Anyone can believe what they see with their own eyes. He knew that belief through faith is more powerful than belief through evidence will ever be. So take heart! Christ has promised blessings upon those of us whose belief rests in faith, rather than evidence.
What's more, there will come a day when everyone will see the proof of our faith. "For now we see in a mirror, darkly; but then face to face: now I know in part; but then shall I know fully even as also I was fully known." (1 Corinthians 13:12 ASV) When Christ returns to us, we will no longer have to struggle with doubt and unsurety. We will have all the evidence we could ever hope for.