These are all apparently life milestones for Cleveland Indians superstar Shane Bieber ... 'cause he told us after the real Biebs mentioned him in a tweet earlier this month -- it was a goal reached!!!

"It was a matter of time, hopefully, if things all went well," Shane told us out in NYC.

If ya missed it ... 24-year-old Shane's had a thing with Justin his whole life -- he tells us he's heard the jokes about sharing the last name with the pop legend since he was little.

In fact, the pitcher even poked fun at the whole situation during MLB Players Weekend last year -- wearing a "Not Justin" jersey!!!

But, the two finally linked up on Aug. 4 ... because after Topps called Shane "Justin" on his baseball card -- Justin responded!!!

"I feel like we have a special connection," Justin wrote.

BOOOM!!!

Shane says the tweet was "definitely surprising" ... and the Indians themselves were so jacked up for the call-out -- they made an offer to the Biebs!!!

"Got an 'I'M JUSTIN' #57 jersey waiting for you at Progressive Field. Swing by and pick it up before your first pitch?"