While I'm sure there are individuals that perhaps struggled with their belief in Hashem and His "existence" were there ever any great chachamim (sages) from the throughout the generations that perhaps expressed their own doubt publicly (in writing, etc. -- whether they came to one conclusion or the other?)
Obviously if one expresses doubts about belief in Hashem he is not a Chacham. But if you mean someone who was once a chacham- Theere is a Gemarah in Berachos 29a:
אל תאמין בעצמך עד יום מותך שהרי יוחנן כ"ג שמש בכהונה גדולה שמנים שנה ולבסוף נעשה צדוקי
Do not be sure of yourself until the day you die, as Yoḥanan the High Priest served in the High Priesthood for eighty years and ultimately became a Sadducee. Even one who is outstanding in his righteousness can become a heretic.
ויוחנן צדיק מעיקרו - Yochanan was originally a tzadik.
The צדוקים (seducees) did not believe in the oral Torah. This is Heresy. This which is against one of the 13 עיקרי אמונה is a subdivision of doubting belief in Hashem. (Heard from R' Moshe Schapiro ZTL).