The Moon forming impact (4.5 Gyr) occurred ~100 million years after Earth's formation. The earliest solid grain comes from another ~100 million years after that (4.4 Gyr). The earliest signs of life (4.1 Gyr) are from ~300 million years after the earliest grain. Does not seem implausible that life could have arisen during the first 100 million years as well. We know very little about that era since the impact liquified the whole surface.