Not really. Using that argument to the non-believer would bring scandal upon the believer as it is easily defeated. Rather as I have stated, the non-believer's claim that
no God exists must necessarily
assume possible existence of God. After all, if I claim there are no rocks, I must have mentally assumed the possible existence of rocks in the first place, else, one wonders, "What is a
rock?"
Further, the corollary of your statement would be that the believer claims God exists by infinite knowledge and is therefore God Himself. No.
Accordingly, argumentation with the non-believer should be more rigorous and great attention applied to their frequent borrowing from the believer's intellectual capital in the arguments they make against the believer. They should not be so easily left of the hook in their duplicity.
What we
know is directly connected to God's revelation. We can exercise our God-given rational capacities, through empirical observation, including science, and from understanding and reflecting upon God's unique revelation—Scripture. Whether one is a
rationalist (priority to reason) or an
empiricist (priority to the five senses), we can trust our
properly functioning senses or reasoning minds because God serves as the necessary epistemological ground of both.
For example, I can
discover the truth that God exists from my ability to reason accompanied by the revelation of that truth via the illumination of the Holy Spirit. We do not invent truth, for God is the author and revealer of all truth. I merely
discover what is true. Yet I remain finite, versus your
infinite, in my discovered
true knowledge—
properly justified true belief—which is also not a mere
assumption that God exists.
Only the believer can properly answer the big questions:
1. What kind of God, if any, actually exists?
2. Is there anything beyond the cosmos?
3. What can be known and how can anyone know it?
4. Where did I come from?
5. Who am I?
6. Where am I?
7. How should I live?
8. What should I consider of great worth?
9. What is humanity's fundamental problem?
10. How can humanity's problem be solved?
11. What is the meaning and direction of history?
12. Will I survive the death of my body and, if so, in what state?