On a particular planet in the Universe, at a certain cosmic moment, the temperature has dropped sufficiently to allow the solidification of many chemical elements; while some elements are still in liquid or gaseous state, the planet's surface may have these general features and components:
This whole planetary environment is the result of many natural processes, events and facts, from the impact of meteorites, asteroids and comets up to the optimum distances from the planet to the central star and the largest planets. After a violent period, the planet's surface has become stable and these environmental conditions remained relatively constant over a large period of time.
The special, maybe unique planet Earth has formed about 4.6 billion years ago and, after a few hundred million years of struggle and instability, it crosses a quieter period that perfectly matches the above stationary profile.
These environmental conditions, along with the hazard of many climatic changes, allowed some natural processes to increase the order of matter and to organize it, to build this way some complex molecular structures. The energy received from the Sun catalyzed these water-based processes, and things continued until a special molecular construction emerged, a stable structure that can spontaneously replicate itself. The next big thing that happened in this context is the process of photosynthesis, and this was the moment when the Oxygen started to accumulate in the atmosphere and to form a protective layer of Ozone (O3). At a later stage, more complex singlecelled organisms and multicellular ones have emerged, and thus Life practically "exploded"; these living organisms consume energy from the environment (oxygen and water, but also light and heat), interact, transform and multiply themselves, spreading over larger and larger areas.
In this huge natural laboratory, where all the chemical elements are practically present, where the movement is continuous and the changes of climate are fast, the number of combinations between different substances is actually infinite; it was only a matter of time until the first cell came into existence - that special structure with distinct properties to be considered a living organism. The odds for this first form of life to appear were very slim. A mixture of substances in precise proportions and a specific sequence of separate processes that happened over a very long time were needed to this end. As the Drake Equation shows, life is very likely to be hosted on many other planets and moons throughout the Galaxy and the Universe (those exoplanets located in appropriate regions, neither too close nor too far away from the stars - the Goldilocks zones). Similar sequences of events can therefore happen in different places, but the life there would not necessarily be identical to that from Earth. Anyway, a very important thing will surely happen after the moment life (of any kind) emerged, wherever and however, namely its evolution.
Note:
Those "building blocks" of life formed in the primordial oceans could have extraterrestrial origins, as the organic molecules could have been brought from the cosmic space by comets and asteroids (panspermia). Simply seen, this thing would only change the place where these molecular structures were born; otherwise, the implications are greater, increasing the odds of other planets/moons in the solar system to host various types of living organisms. Moreover, the chances of life to be more widespread across the star systems, even outside the Goldilocks regions, would increase significantly and therefore the areas to be searched for alien life would thus expand.