The Nyan Cat animation first appeared on YouTube in 2011. The original video was uploaded on April 5, 2011, by YouTube user saraj00n, also known as Sara June. It combined an animated flying cat with a Pop-Tart body, a rainbow trail, and the looping song “Nyanyanyanyanyanyanya!”
The animation itself was created a few days earlier, on April 2, 2011, by artist Christopher Torres, who used the online name prguitarman. Torres first posted the GIF on his website LOL-Comics after drawing a Pop-Tart-and-cat hybrid during a livestream. The character was inspired in part by his pet cat Marty.
The music had an earlier history: the original Vocaloid song was uploaded to Niconico in 2010, and a Momone Momo cover appeared in early 2011. That can cause confusion about the year, but the question asks specifically about the animation’s first YouTube appearance, which was in 2011.