Life is thought to have evolved on Earth about 3.8 billion years ago. If it is true, as many theorist suggest, that the evolutionary process was started by microbes brought to the Earth from space on meteors, then traces of such microbes should still be preserved in rocks from that era if they could be identified. Unfortunately, due the tectonic nature of Earth's crust all such rocks on Earth are thought to be almost certainly destroyed.
However, on the Moon, primordial lava simply cooled slowly over the ages and microbes trapped beneath the surface of ancient rock that landed there may well have been preserved. Test have shown that organic materials placed in simulated moon dust and heated to 700 Celsius survived
These microbes may also be found on other bodies such as asteroids, comets, even other planets like Mercury and Mars.
In fact, Mercury - although it is very similar to the Moon in many ways shows evidence in its composition which suggests it was heated to a much higher temperature than the Moon during its formation, which may preclude it being a source of such evidence. Venus on the other hand, although its surface appears to have been almost completely reformed as recently as 100 million years ago, is thought to be a possible location for find early evidence of life. It is possible that life evolved on a much cooler Venus billions of years ago was destroyed as the planet warmed and its oceans boiled. It is not impossible that parts of the original Venusian crust remain intact below the current surface and could contain a fossil record.
The Moon however, is much more accessible than any of these other locations, making it by far the most attractive proposition for a mission in the near future to find these vital clues to the origin of life on Earth and in the Solar System in general.