The Black Mamba arrived on the scene for the L.A. Lakers on November 3, 1996, against the Minnesota Timberwolves ... going scoreless in just 6 minutes of action off the bench.

Bryant rocked a custom pair of size 14 Adidas kicks as he stepped on the court for the first time ... which he ended up giving away to a diehard fan outside The Forum after the game.

A few years later, the fan was able to run into Kobe again -- and got the legend to quickly sign them outside the team's hotel!!!

Now, the fan is looking to part ways with the keepsakes ... putting them up for auction via Gotta Have Rock And Roll.

We're told these sneakers -- which also come with a ticket stub from the game -- are NOT gonna come cheap ... they have a minimum bid of $100k and could sell for up to $500k!!!

Of course, the 5-time champ went on to eventually score quite a bit in his career -- he's ranked 4th all-time with 33,643 points ... and became one of the greatest players to ever pick up a basketball.