@Mystery_Writer: I think I know what you're saying. Hopefully I'm on the right track.
From a chemistry point of view, there's certain thermodynamic properties that guide whether reactions will occur, which are ultimately derived from the "really, really good theories" of physics (I hate using the word "Law" in laws of physics). For example, say you place an ice cube on a brick road during a hot day in the summer. The ice cube will melt. The ice cube did not choose to melt, it simply obeyed the rules and spontaneously did so. On that same day given the same conditions, you will not see that ice cube spontaneously be reformed. Similarly, this is extended to more complicated assemblages of atoms, such as cells, plants, and even ourselves. We are simply walking containers of millions upon millions of chemical reactions. The astounding part is how we perceive all those reactions, which is another reaction! It certainly doesn't feel like i'm just a more complicated version of an ordinary reaction like salt dissolving in water. What you feel like doing is no more than what the hydrogen atom feels like doing, which is guided by thermodynamics.
So, regarding the hydrogen atom, there will be certain environments in which it will spontaneously react. With the other elements being abundant, and energy being much less spread out back then, you can bet that they will react, or "coalesce", as you put it. These reactions are thermodynamically favourable. Of course, it's much more complicated than that. But the point is that things don't "just happen". The earliest building blocks would have bound, or reacted together, based on those rules. From there, it took off. And these reactions kept occurring, and keep occurring, as the environment changes.
As for "the chance of us existing by chance", I wouldn't know where to start. In my reality, there is no chance. Einstein, and myself, hold a very deterministic view of nature. Some one can crunch all the numbers and reveal that there is a 6.78 x 10^-13 percent chance that life could have formed. However, nature does what nature does. There is only one path it will take at all times. It is hard for us to predict, no doubt. But it is there. Of course, we only assume that nature in past worked the same way as it does now using induction, the glory of science and the scandal of philosophy! But that's another thread for another day!
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