Cell division is a pretty well-known phenomenon. Unless there was some evidence to think otherwise, I would expect it would have quickly evolved to what we see occurring with bacteria. It's possible it may have started through some unknown mechanism that was not sustained long by selection. More than likely though, it resulted from the advantages of budding and cleavage of natural membrane structures as
@Polymath257 and
@Subduction Zone have noted. This is very much a basic description of what occurs with the cell membrane in bacterial cell division. But there is no way to really know the exact details. That does not mean it did not happen, evolve or that not knowing those details means cells don't divide. The latter notion is an extension of the ridiculous logic behind this entire series of pointless threads.
Being a highly conserved essential, cell division is a fundamental feature that is logical to consider having a very early development. And all indications are that it existed prior to the first living things. It is through that division that cells grow, multiply and heritable variation enters a population. Without that variation, evolution would not occur and life would likely have ceased shortly after the first major changes in the environment that negatively effected the population.