An atheist’s question . . .
"Do you ever doubt the existence of God? And if so, why?"
Do I ever doubt the existence of God? Not for a moment. However, an intellectual belief in God’s existence is really a non-issue. This is why: I live in a solid, well-made house. Do I ever doubt the existence of a builder? Not for a moment.
My wife has a well-made and reliable vehicle. Do I ever doubt (for some strange reason) the existence of a car maker? Not for a moment.
I own a well-made computer...I'm sure you get the message. I never doubt that there was a maker of these things, because these things can’t make themselves. My common sense tells me that they had to be made by someone with an intelligent mind. The alternative is ludicrous.
However, the issue I think you may be driving at is rather, "Does my faith in God ever waver?" The answer to that one is the same. Do I ever doubt God? Not for a moment. There’s a reason for this unwavering faith.
If you asked me if I ever waver when it comes to faith in my wife, I would answer the same--not for a moment. This is because I trust her with all of my heart. She is a trustworthy person. She always keeps her word. However, there is a possibility that she could let me down. That could happen because she is a sinner. She is fallible. But God is not. He is without sin, so you can totally trust Him with all of your heart, and you will never, ever, be disappointed in Him.
Life’s terrible circumstances may shake you to the core, but if you catch a glimpse of God’s incredible integrity as well as His ability to keep His word, and therefore you trust Him, your faith will only grow through life's lion’s den experiences. His promises are immutable. They are a solid rock. See Matthew 7:24-25 for details.