While many people might assume that Advance Wars was the first entry in the series, it actually started life on the Famicom back in 1988.
Famicom Wars was never released outside of Japan, and it wasn't until the aforementioned GBA title in 2001 that Intelligent Systems' military series went international.
Between 1988 and 2001, several titles were released on the Game Boy and Game Boy Color, the first of which is now playable in English thanks to a fan-made translation.
1991's Game Boy Wars sees the nations of Red Star and White Moon taking each other on across 36 different maps.
It shares many of the same mechanics which would later be used in the GBA and DS outings and was followed by Game Boy Wars Turbo, Game Boy Wars 2 and Game Boy Wars 3 – all of which were developed by Hudson Soft rather than Intelligent Systems.
You can grab the patch here.