Question

How could life originate multiple times and then rapidly diversify in such a short amount of time?

Just about 600 million years ago, some combination of circumstances led to a sharp increase in the distribution, number, and variety of organisms. The fossils of these organisms mark the start of what geologists call the Cambrian era. This era must have followed a long period of gradual evolution of soft-bodied organisms from single-celled eukaryotes. This evolution produced creatures much like today's jellyfish, which flourished just 50 or 100 million years before the Cambrian era began. There is evidence that this transition from single cells to multi-cellular organisms occurred independently several times; modern organisms did not arise from a single multi-cellular ancestor.

The Cambrian era brought a remarkable acceleration in the rate of evolutionary diversification. Almost four billion years elapsed from the origin of the Earth to the appearance of trilobites. A mere 600 million years after the appearance of these distant relatives of the scorpion, apelike hominids moved from the jungle forests of ancient Africa into the open plains.

Diversification is not only reflected in morphology (the appearance of a creature), but also on the genetic level. As Earth’s environmental conditions changed throughout this time period, the gene pools of populations expanded, that is to say, new versions of existing genes (some better and some worse) appeared as a result of accumulated mutations imposed by the environment. Over time, the production of new genes in this way, conferring new capabilities upon organisms, who in turn faced new and changing environmental conditions, resulted in different types organisms with a diverse range of characteristics and abilities, and hence, morphologies. It is these different morphologies that can be observed in the fossil record, from which we have theorized about the Cambrian explosion.
October 30, 2001