New cases of so-called living fossils do turn up fairly often. Yet they recently were found still living in the south Pacific. Consequently, the vast numbers of living organisms that were already known to be in the fossil record are generally ignored as examples of living fossils. These even include those organisms supposed to be the most ancient of all.
Evolution is supposed to have begun when prokaryotes evolved out of the primeval soup.
Likewise, the primitive one-celled organisms called eukaryotes are supposed to have evolved from prokaryotes. But, these also are still living, essentially unchanged, in the modern world. Simple eukaryotes, resembling living unicellular algae, are first confirmed in the fossil record about 1500 million years ago and first suspected in rocks almost 2000 million years old. The most important modern prokaryotes are probably the bacteria and the blue-green algae, and these certainly should be considered living fossils. They have been found in abundance in 3.4 billion year-old rocks from South America.