Not that I believe in reincarnation, but I don't think this logically follows. Most believers in reincarnation do not accept a steady state model of the universe, so they would probably say that you've lived a finite number of past lives.
And if a bullfrog had wings, it wouldn't bump its *** so much. As Arunma pointed out, the belief in an infinite number of past lives would indicate that the universe has existed for ever. Since most organized religions include a creation scenario, they obviously don't believe that.
Humanino is correct that the question is rather ridiculous from a scientific standpoint.