Lux, there were lots of 3d software before Maya that used the z depth coordinate system. Maya wasn't the first to use it, and it wasn't "changed" for Maya. Cinema4D is one of the oldest, and first commercial 3d software, and came out only 1 year after 3dsmax for DOS. In 1991, C4D's first incarnation was released as FastRay, a software created around one of the first Raytracing render engines. In 1993, Cinema 4D v1 was released on the Amiga. It has always used the Z depth coordinates. This is well before Maya in 1998.

I agree that the Z=UP was adopted first by 3dsmax, because it was conceived from the CAD world, which had always used that 3rd dimension of building up from a flat surface, but I have to question the idea that Maya was the first to use the Z depth coordinate system. What about the software used in the 70s by Ed Catmull, who made the first ever computer generated animation? I'm sure it was using the screen space concept too.