"one celled organisms"Edit: No; by the Cambrian, life on earth had progressed to include many multi-cellular organisms such as echinoderms, trilobites, sponges and small molluscs.
We currently live in the Quaternary, so all modern animals do, too. A few extinct animals that lived in the Quaternary include mammoths, mastodons, woolly rhinos, saber toothed cats, terror birds,...