Complex life is known from the Precambrian. The Ediacaran biota from the very end of the Precambrian and includes a number of complex life forms, including the meter-long Dickinsonia, the triradial Tribrachidium, and the sea pen-like rangeomorphs. Other animals are thought to represent early bilaterians. Complex algae are known from over a billion years ago.
Genetic studies have suggested that other major groups may have records going back into the Precambrian (i.e., arthropods have been suggested to have a Precambrian origin based on genetic data and some trace fossils) but these claims are controversial and the genetic data could be due to this phenomenon where high rates of evolution result in overly high estimated origin dates (you see this with mammals and birds at the K-T).
All the Precambrian-Cambrian boundary represents is the point at which complex life started becoming mineralized all at once and started leaving a better fossil record, and even then that process was gradual (i.e., the early Cambrian "small shelly" fauna compared to the late Cambrian Burgess Shale).