Monsters have always existed. Some are humans, driven mad when their metahuman genes express. Some are animals, with similar genes expressing. The genes that produce super powers seem to be related in some way to the complexity of the nervous system, so bacteria and plants never develop super powers; arthropods almost never; fish, amphibians, reptiles and birds rarely; and mammals most often. Some monsters seem to defy logical origins, and have what seem to be supernatural qualities.
Since it was formed, the IMF has successfully worked to keep the knowledge of monsters from the public, except for the Weekly World News. Monsters of myth, legends and folklore are in many cases based on real creatures. It seems that prior to the IMF, something else was keeping the existence of these creatures from being recognized as accepted, scientific fact.