In one sense, the letter “j” was invented in 1524, but the character was widely used before that—as a numeral.
Here’s the deal: The Roman numeric system used both uppercase and lowercase numerals. When writing a row of ones, writers would often add a slash to the “i" to indicate the end of the series (for instance, the number three would be written as “iij”).
As European languages evolved, they used “i" to represent the modern sounds of both “i" and “j.” In 1524, Italian grammarian Gian Giorgio Trissino wrote an essay that proposed changes to the Italian written language.
That might sound like a pointless exercise, but remember, in the 16th century, literacy wasn’t a near-universal skill. Grammarians’ essays could change the course of a language, and in this case, that’s exactly what happened. Trissino noted that “i" referred to both a consonant and a vowel, and reasoned that “j" could be used for the consonant.
Soon, the “j” was making its way around the world; other European languages adopted the letter, although it wasn’t always used in the same way. We’re not linguists, so we won’t discuss that in depth. However, we will note that Trissino also proposed several other letters, including “v" (which stuck) and “ω” (which didn’t).
Trissino’s contribution was important, but the “j” sound had been part of language for quite a while—it just didn’t have its own letter. That seems absurd in 2019, but at the time, written language simply had fewer characters. Maybe someday in the future, scholars will look back on our time and wonder how we got along without the “ω”.