The oldest (fairly) definitive fossils date from about 3.48 billion years ago (Ga) and consist of sedimentary structures associated with microbial mats living in coastal environments.
Beyond this there are is no known direct fossil evidence so instead we have to rely on geochemical evidence. As the OP mentioned, the oldest known sedimentary rock, the Isua greenstones, are dated to 3.8 Ga and contain isotopically light graphite which may indicate a biogenic origin, although this is hotly disputed.
Recently another paper has pushed the date for potentially biogenic carbon back even earlier to 4.1 Ga. The authors analysed 10,000 zircons from the Jack Hills metasediments from Western Australia and managed to extract one which was uncracked and contained what they believe to be primary, isotopically closed graphite inculsions. The zircon has been dated by U-Pb dating to 4.10 ± 0.01 Ga and so the graphite inclusions must be at least as old as this. Isotopic analysis was done on the carbon and the δ13C value comes out at −24 ± 5‰. This is consistent with carbon which has undergone isotopic fractionation by enzymatic carbon fixation, which has an average value of δ13C = -25‰ over the past 3.5 Ga. Therefore the 4.1 Ga graphite may be evidence of biological activity at this very early stage in Earth's history.