Hard to do this satisfactorily because;
Japanese isn't a kanji-only language. It uses hiragana for word endings and verb conjugations.
There are many kanji-only set phrases, but I don't think there is a set phrase for "no gods, only man" in Japanese. (There might be one in Chinese...).
Inventing a kanji-only translation requires us to think like a Chinese (kanbun) scholar. And, for example, even if I think I have found a good approximation, another Japanese-speaking person may not understand what the phrase is... it will just look like an undecipherable Chinese phrase. Having said all that, and following from the hint you gave, I suggest 無神唯人
As I said, without any explanation, it looks Chinese. Who knows what it might look like to a Chinese person.