I don’t think you can have real faith without questioning.
My understanding of faith may be a little outside of the mainstream, but I don’t see it as being equivalent to belief, or certainty without evidence (or in the face of contrary evidence). I consider it to be more making your peace with uncertainty and living out of that questioning. When you can do that, then the unknown stops becoming an enemy to be vanquished with certitude. Not-knowing becomes the fertile ground of creativity.
The German poet Rilke, in his Letters to a Young Poet, described what I call faith:
“Have patience with everything that remains unsolved in your heart. Try to love the questions themselves, like locked rooms and like books written in a foreign language. Do not now look for the answers. They cannot now be given to you because you could not live them. It is a question of experiencing everything. At present you need to live the question. Perhaps you will gradually, without even noticing it, find yourself experiencing the answer, some distant day.”
I left the religious tradition I was raised in precisely because it considered questioning and faith to be incompatible. I chose questioning, because it felt absolutely essential.