Just look at numbers. Start with zero, add one. You can add one forever, you'll never get back to zero. Cosmology doesn't restrict that.
We also know for a fact that we are made of atoms and particles. Giving infinite time and space, there will eventually be same atoms and particles IN SAME ORDER, therefore our existence is cyclical and not linear.
Speaking of logic, the only reasonable answer would be that we indeed are living in an eternal and infinite space, where big bangs are occurring infinitely without need for cause.
This would also explain the 'free will' problem. Space doesn't care what you think. Its a random generation of algorithms that will make all possible outcomes reality. For an example; I'm president of US in a parallel universe. And in another universe I'm living in a world where star wars really happened. So according to the eternal return theory, we do not have free will.
According to this theory, I will live the same life again and again for eternity. Is this proof that we indeed may be living in hell? A hell we can't escape... ever...