First, I believe the current thinking among cosmologists is that the universe has existed in its present form for between 13 and 14 billion years.
Second, “forever” is another way of talking about an infinite time period, and that’s silly.
Third, just because there differences in energy levels, that’s not a motivation for atoms reacting. Different atoms have tend to be more or less likely to react. Similarly, different molecules have different levels of stability. In addition, some tend to form simple compounds while some can form complex ones. Those which have a valence of one, that is, they have one point of combination such as sodium and chlorine will be stable after they react to form sodium chloride. On the other end of the valence spectrum is, say, carbon, which has four points of combination and can combine with itself to form a wide variety of structures.
The difficulty with the “organism living ‘for an exceedingly long time’” is that there are so many actions taking place constantly, heat, cosmic rays, contact with other compounds, natural molecular instability, organisms absorbing each other, etc. that it’s very doubtful any particular organism will survive for very long unless it’s regenerating itself. For example, when an amoeba absorbs available compounds then splits into two amoeba, we can’t really say that the original one survived.