The initial singularity of the Universe, which is predicted by the singularity theorem, is one of the big mystery in cosmology. I discuss an application of the black hole singularity theorem by Penrose to a
non-singular universe. I found that, under some assumptions, the initial singularity of a universe can be avoidable only when there are compact time slices. In addition, it is found that there is an upper bound to the size of such a compact non-singular universe.