Of course it can be dismissed...by those who don't share such subjective evidence. Other people's subjective evidence is pointless and useless to you and I.
However, getting back to the point, based on such experience or its lack, one can be certain that God exists, or one can be uncertain; it's impossible to be certain that God does not exist based on your personal experience. Within this narrow frame, that leaves one an agnostic (one who lacks knowledge) rather than an atheist (one who is certain that God is nonexistent).
It depends on your definition of God. An omnipotent or Omniscient God can't exist. A supremely powerful and knowledgeable God could theoretically exist.