Nobody should doubt the existence of God. Christian or non-Christian, Rom 1:20. The thing is, the devil will put any thought that affects our walk with God in our head. We have to be really concerned though if he is nailing us on the subject of God's existence, don't you think?
Life, the bottom line is, if we take that leap of faith sincerely, God will catch us. We will land on the other side and be convinced of God's mercy. When you say 'lack if fatih' think about what faith that is. We can have faith in many things. It is not faith in His existence that we need (as we should already have that), rather that He will show us mercy on our sins.
I don't think anyone can deny the existence of God. That wouldn't make sense. Well, I guess some do, but they're silly. I think people more so question our God and who we believe is our Creator.