Some of Nintendo's mascots got their debut on the NES. Some had made their debut on other Nintendo systems.
Kirby's Adventure was released by Nintendo in 1993. This is towards the very end of the NES' life cycle and as such, many people had traded in their NES consoles for a SNES. Kirby himself may have gotten his debut on the Game Boy in 1991, Kirby's Adventure took everything we know and love about the pink puffball and cranked it up to 11.
In this game, Kirby now has the ability to mimic the powers of any enemy he swallows, instead of spits out, granting him powers like Cutter and Spark. Everything we know and love now, all has it's origins in this game. Definitively one to check out.