Your brother oversimplified what Einstein thought. He thought the universe was "finite but unbounded", and an analogy for this is the surface of a sphere (such as the Earth) which has a finite area but has no boundary. Einstein's theory does not itself predict the shape of the universe, but modern discoveries and measurements suggest that in the large scale it has a "flat" geometry which would argue that it is infinite in extent, but nobody really knows.
It is not necessary to have anything "outside the universe" in either Einstein's original thought or the modern understanding. We are used to seeing spheres - balls - in three space but that is no reason to suppose the universe behaves that way, and the mathematics does just fine without it.