No actual evidence, but I get the impression that it was invented by the tiny fraction of Latino people who are at liberal arts colleges in the US, or involved in ultra-niche politics.

“Latine” and “Latin@” (and similar constructions for other -o/-a words) are not unheard of in some actual Latin American countries, though. The former has the advantage that it is straightforward to pronounce in Spanish (I assume for “Latin@s” you’d use the cumbersome “Latinas y Latinos”, and “LatinX” is just impossible).