A young fan got the surprise of a lifetime at her first-ever NBA game Tuesday ... with Russell Westbrook kicking off his shoes and gifting her the sneaks off his feet after the Lakers' win!!

The adorable moment happened after L.A.'s game against the Spurs in San Antonio ... when Westbrook noticed a young girl rockin' a LeBron James jersey and holding a purple and yellow sign.

The posterboard read: "Brodie, can I have your ????" ... and Westbrook was quick to say yes!!