Question

What year did NON-BACTERIAL life emerge of earth?

Answer 1

Single-celled eukaryotes are more closely related to multicellular algae, plants, fungi and animals than is bacteria. 

"The oldest known probable eukaryote is Grypania, a coiled, unbranched filament up to 30mm long. The oldest Grypania fossils come from an iron mine near Negaunee, Michigan. The fossils were originally dated as 2100 million years ago, but later research showed the date as about 1874 million [1.8 billion] years ago. Grypania lasted into the Mesoproterozoic era. 

Another ancient group is the acritarchs, believed to be the cysts or reproductive stages of algal plankton. They are found 1400 million years ago, in the Mesoproterozoic era." 

Multicellular organisms evolved shortly before the Cambrian, during the Ediacaran. The Cambrain explosion, which happened about 540 million years ago, is when practically all living animal phyla evolved. Shortly after the Cambrian explosion, the first fish evolved. Amphibians evolved about 365 million years ago.