In brief, is it linguistically permissible to say that God is "Mawjūd" (existent), even though the word is associated with created time and place, and would saying that He is "not existent" be considered shirk (polytheism)?

It is permissible, according to Islamic law, to say: "Allah exists," and it is obligatory to believe in His existence, glory be to Him. Existence is of two types: self-existence, which is exclusive to Allah, and existence by virtue of another, which applies to creatures. There is no reason to be hesitant about the word "existent" (موجود), because His existence, glory be to Him, is self-existent. It is incorrect to state absolutely that Allah is transcendent of time and place, but it is correct to say that He is "the First and the Last," and that neither time nor place encompasses Him. To say that Allah does not exist is clear disbelief.