Actually, the evidence (assuming evo assumptions) is surprisingly that the theoritical common metazoan ancestor had about the same number of genes as we do, and in fact, "many animal lineages" evolved through "a massive loss of genes" according to one paper (I'd link but the article isn't allowed here).
So there really is no support for the idea:
It didn't start as complex, it evolved into complexity
at least genetically.
Edited by randman, : No reason given.