The conservation law for the total (orbital and spin) angular momentum of a Dirac particle in the presence of gravity requires that spacetime is not only curved, but also has a nonzero torsion. The coupling between the spin and torsion in the Einstein-Cartan theory of gravity generates gravitational repulsion at extremely high densities. We consider gravitational collapse of a spin-fluid sphere into a black hole. We show that a singularity is replaced with a nonsingular bounce if there is no shear. We also show that torsion and quantum particle production during contraction avoid a singularity even if shear is present. Particle production during expansion can generate a finite period of inflation and produce enormous amounts of matter. The resulting closed universe on the other side of the event horizon may have several bounces. Such a universe is oscillatory, with each cycle larger in size then the previous cycle, until it reaches the cosmological size and expands indefinitely. Our universe might have therefore originated from a black hole.