If you work backwards using a mean Hubble Constant of 70 (7% of the distance between unbound objects per billion years) then you are left with about 35% of the original distance - not a singularity. If Cosmic inflation was in the order of a large galaxy in size, then we would not see any CMB as it would all have passed us by in less than a million years after the recombination event that created it. After 13.5 Billion years we can still see galaxies that formed 300 million years after the CMB was created. In an expanding universe these galaxies must have emitted the light we see them by when they were (only) about 9 Billion light years away and it has taken 13.5 Billion years to reach us as it travels through expanding space. Our optical evidence that we can still see these galaxies puts a lower bound on the extent of Cosmic Inflation of about 9 Billion Light Years. There is no observable upper bound on Cosmic Inflation and the Observable Universe was only 18 (9+9) Billion Light Years across when it emitted the farthest light that we see today. So many a Cosmology Text needs a serious re-write.