There are a couple of "explanations" for the Cambrian explosion.
First, this so-called "explosion" took place over several tens of millions of years -- hardly instantaneous, and certainly not consistent with the Genesis account.
Second, as you point out, there is a much longer fossil record that extends much, much farther back before the Cambrian. Also, the current genetic evidence indicates that the splitting of the major phyla occurred well before the Cambrian.
Finally, there is not a single example of an indisputably modern life-form that is found from the time of the Cambrian explosion. Even those species that can be identified with extant taxa are very different from the modern forms.
In short, there is nothing to explain. In fact, it is the YEC who has to explain why, if this is supposed to be a record of the Genesis event, why there are no modern life forms, why life forms are dated much earlier than the Cambrian, and why the Cambrian Explosion is dated to a very wide range of time -- the same explanations that the YEC has failed to provide to geology in general.
Speaking personally, I find few things more awesome than contemplating this vast and majestic process of evolution, the ebb and flow of successive biotas through geological time. Creationists and others who cannot for ideological or religious reasons accept the fact of evolution miss out a great deal, and are left with a claustrophobic little universe in which nothing happens and nothing changes.
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M. Alan Kazlev