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The Century Dictionary and Cyclopedia defines Singular as meaning:

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

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 actually overtook singular phenomena in popularity 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.

This chart demonstrates the popularity of singular event vs singular phenomena. Both were very popular in the 1820s but declined usage until the 1940s, but afterwards singular event began to rise in popularity again while phenomena remained stable, making Singular event the more popular form by a few times over.

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.