Is it rare or common in the universe to have a primordial soup spawn individual organisms competing for natural selection, instead of a single, giant organism, evolving as a whole?

Although sci-fi writers have done well to stretch the imagination as to what alien life might look like, they often project or extrapolate from creatures we know on Earth, such as reptile men or urchin-headed beasts. The more creative ones imagine floating ethereal tablets communicating telepathically, but even that is a projection of Earth-like individual organisms.

Is it possible to imagine life without individuality? Could alien life on another planet from start-to-finish be a single organism, possibly with internal independent parts that undergo natural selection, but ultimately combining into one piece? One planet, one life. Perhaps the alien life is fused with the planet itself, such that the entire planet is one organism. In which case, we may be peering into a universe looking for life on other planets, when the planets themselves might be peering back at us as floating eyes off in the distance, and together a series of organ-like planets in a solar system might form a single organism. Who knows, and we can't know because we are forever biased by life as we know it.

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Star systems interact so slowly that we wouldn't know whether life is evolving on a celestial scale or not

Even if there were no small molecules in our universe, and all that existed were just asteroids, moons, planets, stars and galaxies, then given enough time, the planets would form the building blocks of life. Right now, the only visible loops are spinning gravity wells, like galaxies and solar systems. But given enough time, binary star systems could interact with other binary star systems or galaxies in an elaborate dance, eventually creating patterns that could build quasi-proteins which could lead to mobile creatures, nervous systems, and eventually intention. It may take a power-tower number of years—beyond the theoretical Heat Death of our universe—for these celestial dances to map to the same dances that occurred in Earth's Primordial Soup, but eventually a pattern other than spinning gravity wells will prevail. So long as there is time, then patterns that persist shall.