I didn't fully articulate my hypothesis. I am proposing that this "same DNA structure" will appear in all these independent original organisms that form during the same time period.
Yeah, that's definitely possible, but what prompted you to believe this? So, the primitive nucleotides of the very first cells spontaneously evolved in different parts of the earth. The premise is used by astrobiologists to rationalize alien life on far away earth-like planets.
So my hypothesis has been put forth? I'm not surprised, as it seems not only plausible, but likely.
What prompted me to believe this you say. Well, I'm going to have to get a little philosophical; I hope you don't mind. Most theists believe the first humans were created by god. Theists who accept evolution would say god created the first life form then did something special to make us (gave us souls). Many, if not most, atheists believe life likely (not certainly) formed on earth by accident. I myself am an agnostic/deist (of a certain sort). I believe (but am not certain) that the universe was designed by intelligent agency. What that agent(s) is I have no clue.
Einstein was an agnostic/deist (or a certain sort) as well. He presupposed the existence of a "superior reasoning power" as he was developing his theories. He would say, if I am god how would I create a universe, etc.
The universe is governed by a limited set of rules/forces that exhibit profound order, regularity and harmony in the way they function together to produce highly creative effects upon matter/energy. Using the language of mathematics we describe the way these rules/forces manipulate and direct matter/energy and arrive with precise, logical, elegant laws.
As I stated prior, stars, planets, moons, blackholes, atoms, subatomic particles, elements, etc., are inevitable consequences of these governing rules/forces and they exist in the same manner all throughout the universe, wherever we observe. Whether you presuppose a designing agent(s) or not that crafted these rules/forces when pondering how life emerged, it is still reasonable to assume that life too is an inevitable consequence of rules/forces as well when considering all these other forms of matter/energy.
If it's true that life is an inevitable consequence of governing rules/forces that doesn't mean that the universe was necessarily designed. However, in my opinion this would be circumstantial evidence that favors design.
If my hypothesis is true then life all throughout the universe would have the same foundational biological components. If we were to discover life on other planets and confirmed this to be true that would be empirical evidence that supports my hypothesis.