According to the theory of Cambrian explosion most of the animal groups found today appeared for the first time some 545 million years ago within a short period of 5 to 10 million years (this is indeed short for evolution). Life existed on Earth 4 billion years ago but the organisms present at that time were mostly bacteria, Planktons and some multicellular algae. About 600 million years ago in precambrian age there was a rapid change as evidenced by fossil record.Then, between about 570 and 530 million years ago, another explosion of diversification occurred, with the eventual appearance of the lineages of almost all animals existing today.
The main problem with so called Fossil record is the data which is available through fossils but some early organisms may have escaped fossilization either due to their body form or could be because of environment they lived in. Interpretations of this critical period are subject of lively debate among scientists like Stephen Jay Gould of Harvard University and Simon Conway Morris of Cambridge University.
Image credit: Openstax Biology