Time is an integral component of the universe as we know it.. They are not independent, one cannot exist without the other. The statement is not coherent, since it implies a separation which is not real.
Outside the universe is a state of infinity. Whatever the universe came from has always existed and will always exist. There is no time in such a state. Time only comes into being as the universe comes into being.
Context would be nice, but in the absence of context, we can use some basic physics. Any point in the universe is described by three space coordinates and one time coordinate. So, time exists at every point in the universe.
The universe as described by Einstein has a fancy name - a Riemann manifold - possessing the 4 spacetime coordinates mentioned above. A manifold such as this is not required to be embedded in anything and therefore there is no need - or meaning - for an external set of coordinates to describe the universe, obviously including the time coordinate.
So time exists within the universe but since the universe is not embedded in anything there is no meaning to the notion that the universe exists IN anything, including time.