I believe in the existence of extraterrestrial life, the: living organisms found in the outside of the solar system.

Changed your comma to a colon, since here, "living organisms found outside of the solar system" is defining "extraterrestrial life".

"Found outside of" is more natural than "found in the outside of".

Existence of aliens deserves further research, e. Even scientists are not sure about the presence of extraterrestrial life.

These should be two separate sentences.

From my perspective, Tthe probability of extraterrestrial life is very high.

Thanks to the work of astronomer's works, we can argue thatfor the presence of hundreds of millions of galaxies in our universe.

Use "the astronomer's" when you're referring to a specific individual. If it's general, use astronomers (plural).

"We can argue *that* the presence of..." is an incorrect use of "that".

Either of these would work:
"We can argue that there are hundreds of..."
"We can argue for the presence of hundreds of..."

Every single galaxiesy has countless stars.

Changed to singular.

This is why I believe in aliens.

Or "This is why I believe aliens exist."

The universe is too big for the mankind and the creatures on the eEarth.

I don't know how to explain why it's not "the mankind" and why it is "the creatures", but the correction would be the natural way to say it.

Usually capitalize Earth when you're talking about planets, stars, etc.

Now scientists believe that living organisms emerged bythrough the process called chemical evolution.

As a counterexample, some scientists argue the fact that mankind sent so much amount ofany radio wave to thes into space for over 200 years.

But no one recognizes it.

So maybe it indicates there is no intelligent ince 200 light years away from eEarth.

Or "So maybe it indicates there is no intelligent life 200 light years away from Earth."

However, this argument cannot back up the inexistentce of life up.

This sentence needs the noun form: inexistence.

Inexistent is used as an adjective, e.g. "His inexistent love life."

You can say "this argument cannot back the non-existence of life up", but "this argument cannot back up the non-existence of life" is more natural and easier to understand.

Bottom line, Eeven if there is no extraterrestrial life within 200 light years of Earth, I believe in the existence of aliens because the universe is so large and life can be created from compounds.

I believe in the existence of extraterrestrial life, the living organism found in the outside of the solar systems beyond our planet.

extraterrestrial life is living organisms beyond our planet, including within our solar system

Existence of aliens deserveThe question of alien existence merits further research, evenas scientist not sure abouts remain unsure of the presence of extraterrestrial life.

From my perspective, Tthe probability of extraterrestrial life is very high.

Thanks to the aAstronomer's work, we can argue thestimate the presence ofre are hundreds of millions of galaxies in our universe.

Every single galaxiesy has countless stars.

single = galaxy
plural = galaxies

This is why I believe in aliens.

The universe is too big for the mankind and creatures on the earth.

I am not sure what you mean by this?

Now, scientists believe that living organism emerged by thea process called chemical evolution.

ItThis means life can be made from chemical compounds.

As counterexample, some scientist argue the fact that mankind sent so much amount of radio wave to the space for over 200 yearsSome scientists disagree with the possibility of extraterrestrial life; they argue that the possibility is unlikely as mankind has sent radio signals to outer space for over 200 years without response, indicating there is likely no intelligent life within 200 light years from earth.

We don't typically use the word "counterexample". Additionally, if you say "on the contrary", "on the other hand", etc, the sentence that follows needs to have the contrary fact/opinion - this sentence is just a fact that is not contrary to anything.

But no one recognize it.

see above

So maybe it indicates there is no intelligent in 200 light years away from earth.

see above

However, this argument cannot back the inexistentce of life up.

This is a very colloquial/spoken way of saying this.
For a written/more formal approach, you might say "However, this argument does not exclude the possibility of existence of extraterrestrial life."

Bottom lineIn conclusion, Eeven if there is no extraterrestrial life within 200 light years of Earth, I believe in the existence of aliens because the universe is so large and life can be created from compounds.

Also "Bottom line" very colloquial/spoken, not grammatically correct for proper writing.