After cleaning his room, Keita Takahashi (Katamari Damacy, Noby Noby Boy) found this poster that, according to his blog, “was made when Katamari was displayed as [a] reference exhibit at [the] Japan Media Art festival.” He also points out that "you can see [the] copyright at [the] bottom of [the] signboard and it says '©2002'. Wow, I've forgotten, this year is [the] 10th anniversary since [the] prototype!"
In the 2003 incarnation of the festival, Katamari Damacy was selected as one of the Jury Recommended Works.
A Game Developer magazine post-mortem listed the game development time as 1.5 years and, given the release date of March 18, 2004 in Japan, it would put the anniversary around September 2002, a few months from now.
But Katamari was prototyped through Namco’s Digital Hollywood Game Lab (whose logo can be seen on the poster), which is a game development education program run by the company, before becoming the game it is today.
So the exact date may be unclear but have a brighter day: Use this as a reason to revisit to Katamari Damacy today.