Justin Bieber -- Takes Mystery Girl to NBA Finals ... DAYYYUM!! [PHOTO]

Justin Bieber tried to impress his Miami mystery date by taking her to Game 7 between the San Antonio Spurs and Miami Heat -- but based on some pics he screwed it up.

It's unclear if things are serious with this new chick -- who seems older than Selena Gomez, and is definitely WAY more endowed!

JB was spotted around Miami with her before the game ... and sitting next to each other in a luxury box during.

Here's the thing ... if Justin really wanted to impress her, he wouldn't have worn those neon sneakers.