Congratulations! So far, you are the only one brave enough to think about the problem. You are correct in your observation that such a statement as the cosmologists make, "Before the Big Bang there was no time," is logically contradictory since the word "before" requires the existence of time. This, however, is only a problem for materialists who believe that matter and its motion are all there is. It is not a problem for Creationists who believe that there is a reality beyond this physical universe.
If, therefore, there is a reality outside of this universe there can be a cosmological "before time."
Good question, good thinking.
It is not a problem for Creationists who believe that there is a reality beyond this physical universe.
Such a belief raises more questions than it answers as attempts are made to describe such a "reality" without reference to time or space. We are asked not only to accept something unobservable and incomprehensible, as space and time are inherent in all of our ideas. Then we are to suppose that the makings of things as complex as consciousness, sensory preception, and actuation are contained in this incomprehensible "reality". In short, we must simply accept what does not make any sense.
So the pursuit to explain the universe does not end because it is explained, but because it becomes inexplicable.