The IMI Uzi made its debut in The Ballad of Gay Tony, but was first planned to be included in the first expansion, The Lost and Damned. It shows up in various artworks for the game, usually being held by in-game character Angus. However, unlike The Ballad of Gay Tony's Uzi, this one is not solid gold.
The Israeli Military Industries UZI was once intended to be the signature weapon of the Grove Street Families, lasting until the game's beta version, but was replaced with the MAC-10 and reassigned to the Ballas gang with the TEC-9 taking its place in the Grove Street arsenal. The Uzi model can still be found in the game, as a statue of Big Smoke is holding the weapon, along with a shotgun, on the top floor of Big Smoke's Crack Palace. UZI was also originally present as a usable weapon in GTA Vice City. It's possible it was used as a placeholder.