The PSX was released in Japan on the third of December, 1994.
Here is a list of games released for the PSX on December 3rd,
1994.
Crime Crackers (SCEI) *note* Crime Crackers was made by Sony,
while all of these games were released on December 3rd, Crime
Crackers was probably the "first game ever" as it was in
development specifically for the PSX.
Ridge Racer (Namco)
A. IV Evolution (Artdink)
Gokujor Pardius Da! Deluxe Pack (Konami)
Mahjong Goku Sky: Atsushi (Victor)
Mahjong Station Mazin (Sunsoft)
TAMA (Time Warner)