Even more so, the moon is slowly moving away from the earth. A couple of million years ago, it would have completely covered the sun. In a couple of million years, it will not fully cover the disc.
A million years is a long time for humanity, but a blink on the timescale of moons and stars. We didn’t just luck out with the moon’s large size, but also with the timing of our evolution.
Life will almost certainly be fairly common, given the right conditions. On earth, it seems to have appeared not long after conditions made it possible. We either won the lottery on the first week, or the odds aren’t actually that bad.
The problem is, we can’t detect life right now. We can only see potential communicating civilisations. These are a lot rarer. We currently know of 1, humanity. That will change in the next few years. We have telescopes being designed/built capable of detecting the gasses in the atmosphere of an earth sized planet. While we won’t recognise all life types this way, a lot will show up in abnormal gasses, e.g. free oxygen. This should help bound the possibilities a lot.