The fair answer is: Muslims do not deny proof; they deny a cramped idea of proof that treats God like a chemical in a lab. The Quran gives rational signs, appeals to the fitrah, and argues that created things point beyond themselves to the Creator.
Why the question has real force
The objection is strongest when aimed at someone who says, "God cannot be proven," rejects philosophical arguments as unreliable, rejects empirical arguments as irrelevant, and then still demands belief. In that case the critic can reasonably ask: if all proofs are dismissed, what separates faith from mere assertion?
That is a fair challenge. If a person truly denies every kind of proof, then he has no right to claim he has proved anything. But that is not the Islamic position. Islam denies that God is one object inside the universe to be measured alongside other objects. It does not deny that His existence is known through sound reason, innate recognition, and revelation.
What the Quran actually presents
The Quran repeatedly calls its arguments "signs" - not vague feelings, but pointers that reason can grasp. One of its sharpest arguments asks:
"Or were they created by nothing, or were they the creators of themselves? Or did they create the heavens and the earth? Rather, they are not certain."
Quran 52:35-36
This is simple and powerful. Things that begin, change, depend, and perish do not explain themselves. The universe is not a necessary being; it is composed of dependent things. To say it came from nothing is not an explanation. To say it created itself is contradictory. The best explanation is a necessary, uncreated Creator who gives existence to what depends on Him.
The Quran also argues from order and oneness:
"Had there been within them gods besides Allah, they both would have been ruined."
Quran 21:22
If ultimate lordship belonged to competing independent gods, creation would not have the unity, consistency, and governance we observe. The world bears the mark of one supreme will, not rival absolutes.
Not every proof is a laboratory proof
Some truths are known without microscopes: that other minds exist, that the past is real, that moral responsibility is meaningful, that reason itself should be trusted. These are not irrational; they are known through a broader use of reason. Belief in God is like that, though greater: it is supported by fitrah, reflection, and the signs of creation.
"Every child is born upon the fitrah, then his parents make him a Jew, a Christian, or a Magian."
Sahih al-Bukhari and Sahih Muslim
The fitrah is not a substitute for thinking. It is the natural readiness to recognize the Creator, which can be covered by habit, desire, trauma, or bad teaching. The Quran does not say, "Do not think." It says to look, compare, remember, and reason.
What this proves, and what it does not
This argument establishes that belief in God is not a blind leap. It gives strong rational grounds for an uncreated, necessary Creator, distinct from the universe, powerful, knowing, and one. It also shows that atheism has its own burden: it must explain why anything exists at all, why the universe is intelligible, and why dependent reality needs no ultimate explanation.
What it does not do is put God's essence under human control, or force every stubborn person to submit. Nor does it, by itself, prove every detail of worship, law, and the Hereafter. For that, the next question is revelation and prophethood, especially the truthfulness of the Prophet Muhammad (PBUH) and the Quran.
So the answer to "What is your proof if you deny proofs?" is: we deny false limits on proof, not proof itself. The signs are there, and the mind is invited to read them honestly.