If you were born into a large room where no one had ever been outside or seen outside, no one inside could prove the existence of God, not scientists, not scholars, no one. In this same way the only way anyone can have proof or knowledge of God's existence, is if the information comes from the outside in (so to speak). That is what the Bible is. It is a written record and the witness of many who have heard directly from God, who know for certain of His existence.
I am such a witness.
We either hear their report and witness and believe it, or we do not. If we do, God then decides whether or not to add to that person the same personal encounter, or not. But rest assured, just as you have read, He esteems those who have not seen but believe greater than those whom have seen.
The real question though, is not whether or not there is a God. But rather, am I merely organic, or eternal? If eternal...then it is best to get to know Him by all means.