There's a little more to it than that. Okay, there's a lot more to it. It's an incredibly complex process. In addition, it's not known if life originated from one source, or whether it sprung up as several origins in different areas. There still remains a lot of unknowns. My bet is that life began independently on the planet as a result of the right combination of conditions and ingredients. Whether these molecular ingredients resulted from materials on the planet or were delivered from space during the Bombardment period is unknown. Either way, the ultimate origins would've still been celestial. We know organic molecules exist in space.
But the question is whether life on Earth is basically a gigantic organism (or organisms) that's continuously expanding into multiple parts. In a way, that's sort of what's happening. After all, you are the result of combined cells that originated from your parents, and they in turn from their parents, and so on. However, each successive generation is not an identical copy of the previous generations. It's a blend that produces unique changes to each individual although those changes can be extremely small. That's partly why DNA is seen as a "fingerprint" that's unique to each person. Even identical twins have some variations. The only thing that could be considered identical at the genetic scale would be clones. However, the offspring of clones would not be genetically identical unless clones are made from the clones.
The point is that it can't be so easily defined as one huge organism, but rather as multiple organisms which are the result of multiple processes that technically started with the Big Bang. In other words, we're also related to stars and galaxies. So can we say the universe is an organism? No. The universe is an environment that happens to allow for the conditions and processes for life to life to develop.
So what are the processes that replicates life? I posted some short animated clips on another thread that might help understand what's going on.
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