Whether people believe in a created creator or not is not relevant to whether that is the case or not.<quoted text>
The creator would be necessarily independent of time because time's existence was inititiated by an act of the creator, namely, the emergence of the universe in which time is defined.
If the creator was created, such an event would still be independent of time, as time would not exist except for the action of the created creator.
More to the point, nobody believes in a created god, so nobody believes that type of god exists.
The cyclical universe model you imagine does not help the problem of a caused universe and the traversing of infinite time. It relocates the necessity of a cause further in the past, and the infinite cycles would mean that our present cycle could never occur, and we would not exist and not be discussing it.
I see what you are saying about a creator and the idea of a first cause, but the very idea of a first cause necessitates the insistence that a cause wasn't itself caused because someone finds it emotionally satisfying to declare something "first". Anyway, the cyclical universe in my example was infinite, and was never "caused". I don't see why time can't exist and yet be infinite any more than space might be infinite and yet we still can measure parts of it.