If you define the word time in such a way that it only has meaning in the context of our universe, then the concept of a time before the universe doesn't make sense. But if you do that, then there may need to be a new word to define time outside the context of the universe.
If you picture the universe as a basketball passing through a flat plane, the big bang is the precise point that the ball touches the plane. Then as the ball passes through, the touch point becomes a small circle, then a bigger circle, all the way up to the full 29.5 inch circumference. Then it would contract back down to a single point and when the ball had fully passed through the plane, it would be gone and never come back.
If you were to describe how long the basketball existed, you could define it in several ways. You could talk about the ball moving at a pace of one inch per 1000 years. You could ignore the size, and just say it lasted for 9500 years. Or you could ignore the speed, and just say it lasted for 9.5 inches. That last measurement might be the most meaningful, at least for the people in the universe. Even though its hard to picture our universe as existing for a certain number of inches, or light years, or some other distance, its easier to envision time as a dimension when you compare it to other dimensions. And in the sense that the universe existed for 9.5 inches, and we were constantly moving vertically through the basketball in such a way that we could measure how many inches we had gone so far, we might be somewhere around four inches right now.
In that context, talking about something before or after the basketball wouldn't really make sense. We only exist in the sphere of the basketball, and time for us began the moment the basketball touched the plane of existence. So there is a beginning and an end to time, if we define time in that way. But in the context of a plane that existed before the basketball and will exist after it, and which may have other basketballs or baseballs or snow cones passing through it, it absolutely makes sense to discuss time before the basketball and after the basketball.
Now imagine that instead of the basketball passing through the plane, you are the plane, passing through the basketball. You're the one moving through time. The basketball always is and always was exactly that shape. In fact, imagine that you're not moving. You're outside the basketball, viewing the whole thing, but its so big you can only look at one cross section - just one dimple of one cross section at a time. That's you, not moving through time, but with a perception of movement due to your limited ability to see the whole universe and everything that ever was and ever will be all at once. In that context, time doesn't exist as a unit of measurement, but as a unit of perception by a limited observer, in much the same way that the pay binoculars at the top of the empire state building only see a small swath of the city at any given moment, but it would be absurd to measure new york city in quarters to explain how many quarters you have to put in to see the whole city.