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I've read this question, but none of them are what I am looking for. I once read a book that used a word to describe an event that has happened in the past, but the odds were so astronomical that it will likely never happen a second time. The context I read these words in were the creation of the first life on earth (without any theological ideas). Basically, the text said that the scenario for the creation of the first living organism happened on a planet where conditions were just right by complete chance, and that the odds of this were so astronomical that it would likely never happen again anywhere in the universe over any length of time.

Sample sentence: "The creation of the first organisms was incredibly unlikely, the event can be called a _________ event, or an event that will likely never happen again."

I can't pretend to understand the validity of the claims by the text, but the words they used to describe these events were quite clever (and scientific sounding) that it would make a fun hyperbole.

I thought it was something along the lines of singularity event, but that doesn't sound quite right.

The Century Dictionary and Cyclopedia defines Singular as meaning:

7. Out of the usual course; unusual, uncommon; somewhat strange; a little extraordinary: As a singular phenomenon

More literally it derives from single, meaning one, so a singular phenomena is logistically something that is assessed as happening just once. It is of course possible to use the term hyperbolicly or mistakenly, which can diminish the effect, but I doubt you will find any word that lacks that particular problem. The nature of hyperbole is that people tend to exaggerate, and sometimes intentionally, so they will choose whichever word most effectively achieves the exaggeration they want to convey.

Since the dictionary entry was written, singular event has grown more popular than phenomenon as shown by Google Ngrams, and Collins shows that singular is one of the top 10,000 words used in the language, so I figure that this demonstrates that it is more than common and easily enough understood.

An example of relevant usage used in a context regarding the unlikely creation of life can be found on page 3 of Free Radicals: Biology and Detection by Spinn Trapping et al (1999):

This biblical account of creation [referring to an excluded quotation of Genesis 1:1–7], a theme common to the cultural life of many societies over the past several millennia (Westerman, 1974, foretells the birth of life on our planet. From the available evidence we have today, this epic began about 15 billion years ago, when, we are told, a massive explosion of incomprehensible power, referred to as "The Big Bang," created everything that was, is, and will be (Hawking, 1088; Peebles et al., 1994). From this singular event, the evolution of life commenced with the formation of hydrogen and, to a lesser extent, helium.

Regarding ❌singularity event, the reason that does not work is because the -ity suffix functions to change the adjective into a noun, as noted by the entry for -ity:

A common termination of nouns of Latin origin or formed after Latin analogy, from adjectives, properly from adjectives of Latin origin or type, as in *activity, civility, suavity etc., but also in some words from adjectives not from Latin origin or type, as in jollity. The suffix is properly -ty, the preceding vowel belonging originally to the adjective. See -ty².

Sometimes adjoined nouns do modify nouns, but much more rarely than adjectives and in a very different manner.

The creation of the first organisms were incredibly unlikely, the event can be called a one-off event, or an event that will likely never happen again.

Merriam Webster defines it as

limited to a single time, occasion, or instance

A witty alternative would be once in a lifetime but I find it rather confusing in this context. It might work for shorter timescales, though.

Unique.

Unique means ‘singular, or only happening once.’

It is from the word one - etymology - ‘early 17th century: from French, from Latin unicus, from unus ‘one’.’

A unique event. One that happens only once.

Unique has also been broadened to mean ‘unusual or rare’ but then, things that only happen once, generally are that.

https://www.thefreedictionary.com/unique

Two other suggestions. First, there is the latin phrase sui generis meaning the same as "singular" or "one-off" (see other answers).

For the most extreme degree of unlikelyhood short of actual impossibility, there is the scientific phrase "a thermodynamic improbability". This refers to an event which is not actually forbidden by the laws of the universe, but which is so exceptionally unlikely that it will "never" happen -- unless the context is an infinity of time and space, in which case it is certain to happen, because infinity divided by any finite number is still infinite. An example would be one's head spontaneously falling off, simply because all the atoms comprising one's head happened to vibrate in the same direction at the same time.

Perhaps isolated, as something that shouldn't happen again, but does not guarantee it will not reoccur:

"The high school students assured their principal that the cafeteria food fight was an isolated incident, promising that it would never, ever happen again."

www.vocabulary.com/dictionary/isolated

Used in medical terminology as well:

"Isolated occurrence means a single event which a physician concludes with reasonable medical certainty will not recur in the future"

www.lawinsider.com/dictionary/isolated-occurrence