What are the requirements for a word to have an etymology?

Etymology is the study of the history of words. By analogy, the history of a word is also called its etymology.

If a word exists, it has a history, however short and irrelevant it may be. In other words, every word has an etymology.

I just invented a new word in my head. Even it has an etymology: its history is that I just made it up, didn't tell anyone, and will soon forget it.

Whether a particular editor of a particular edition of a particular dictionary thought the word was important enough to include it in the dictionary is a completely different question, and whether the etymology of the word is known with enough certainty that the editor feels comfortable to present it as fact in a dictionary is yet another.

Here's an example: German has five main vowels, a, e, i, o, and u (not counting the Umlaute ä, ö, and ü). German has the words "Schlacht", "schlecht", "schlicht", and "Schlucht", accounting for four of the five vowels, but the word "Schlocht" does not exist. Also, in Germany, it is customary to have some sort of separator that you put on the conveyor belt on the checkout counter in a supermarket to signal that the next stuff on the belt belongs to the next customer. However, if you were to ask a random person, they would not know what this thing is called.

So, one evening after having a little too much too drink, an acquaintance of my parents' decided to fix what he perceived as two "holes" in the German language, and, killing two birds with one stone, declared that he names the thing nobody knows what it's called "der Schlocht".

Nobody else except him uses that word, but it still has an etymology: a bottle of Pinot Grigio. (I'm guessing. It might have been red wine.)

(Apparently, that thing is called a "Warendifferenzierungsmodul", "Warentrennstab", or "Warentrenner", but I will have forgotten that in a few days.)