Completely false. There are lots of fossils from the past and biologists have determined that the rates at which animals are observed to be fossilized in the past is the same as is the case now. It's called the science of taphonomy and provides very accurate estimates based on currently observed physical processes regarding which ancient rocks are going to be fossil rich or fossil poor. You seriously don't think that paleontologists run around the globe and come across fossils by blind luck do you. Here is an excellent example as to how physical processes today unerring guide scientists to discovering evidence regarding the past showing the uniformity of laws of nature through time.Not at all. They are.
In the former nature man and most animals likely could not leave remains. From dust to dust real fast. Only some creatures for whatever reason, could and did. The fossil record is therefore a record of a tiny tiny tiny slice of all the life on earth that lived!
After the nature change which was probably a little after the flood (1-300 years) we could leave remains.
Taphonomy & Preservation
preservation
Book on taphonomy
Taphonomy