When a believer is taught that God hears his cry for help and then finds out that that is not the case, a sense of desperation may set in. A non-believer does not have that problem.
When gross overwhelming injustice happens and we are powerless. We all cry to God. Although the picture/image/sense of what we are crying to may vary with one's explicit beliefs. The atheist may, for example, imagine he is calling out to Justice or decency or the universe, but ultimately we all cry to God. As Descartes noted, we have an innate idea of Him--although it can be prejudiced and confused by our experiences.
A believer has hope and the nonbeliever has none?
Or... it is better to have no or little hope than to “foolishly” and “naively” have hope?
Faith = hope.
Yes and that is why Paul said that if our hope is in this life
only we are most miserable of all men, even unbelievers.