I haven't put a lot of study into the Cambrian, but I don't think it's all that much of a mystery. The creationist websites make a big deal of it, as if it boggles everyone's mind, but I don't think it does. It followed an ice age, and perhaps a mass extinction, so there were mostly empty niches that could be filled. The appearance of several new body types wasn't all that sudden, certainly not "at the same time." The Cambrian period involved millions of years, which for primitive animals is tens or hundreds of millions of generations. And not every body type appeared in the Cambrian. Mammals, reptiles, birds, and even insects, for example, came later. But it was a time when several new types appeared, and contrary to what you may have heard, ancestral forms have been found in earlier strata. Nothing about the Cambrian contradicts the theory of evolution. Nothing quite as productive has happened since, because when vacant environmental niches get filled with flourishing species, in the absence of another mass extinction it's difficult for several significantly new types to get very far without becoming food for something already there.
Humans 'fill' all kinds of 'niches' as well, and we've evolved nothing to be able to do so.