What was the process that created earth's first atmosphere and ocean water?

Answer 1

Cometary and meteor impact along with extreme volcanism.

The initial atmosphere of the earth was rather akin to Venus, although the impact that helped form the moon got rid of a lot of it. Afterwards the atmosphere was mostly the result of volcanism along with gases brought in with comets (see below).

Water arrived mostly from the comets Jupiter and (to a somewhat lesser degree) Saturn tossed our way during the Heavy Bombardment period as they stabilized in their orbits.

This lead to a cooling of the surface and the formation of oceans. Exposed rock soaked up some of the CO2 and other chemicals in the air, and were then recycled back into the mantle, where some chemicals were more or less likely to break down and be bound to other chemicals - perhaps to stay in the mantle, perhaps to be re-released during volcanism.

When life arose in the seas it began to alter the atmosphere more extremely yet. It sucked up a lot of CO2, leaving it in the silt of the sea bottoms. It also released a lot of O2 - a poisonous waste gas. Eventually the O2 was high enough that life had to adjust to it: either learn to use or ignore it, or die or find shelter where it did not exist. Anaerobic bacteria (that which dies with oxygen) is still with us today, but it now in the extreme minority. Most life learned to endure and later thrive with O2 - and as a result the atmosphere became ever more O2 compared to CO2.

During the Dinosaur era O2 was around half what it is today and CO2 was around almost 10x what it is today. In modern times O2 remains relatively stable, but CO2 still jumps around a bit. Since measurements started taking place in the early to mid 1800s CO2 has ranged from about 250 ppm (during the 1890s) to about 500 ppm (during the 1850s). It seems to rise and fall over about 80 years or so, usually a few years following similar temperature trends. In the present its around 350 and still rising, although temperature trends have been falling for about ten years. If it follows the normal pattern, in about 10 to 20 years the world will be quite cooler and the CO2 will start to fall, as natural and expected by many scientists.