Parent wants to push lonely tween to work on making new friends

My older son (12, seventh grade) is awesome. He’s smart, funny, creative and kind. However, he doesn’t have any very close friends or a best friend, and he really wants that. There’s a group of kids he hangs out with, but he’s mostly on the periphery — goes to big group activities but is never invited to smaller activities like sleepovers. He plays sports and is friendly with his teammates, but, again, things haven’t really clicked there.
I’ve encouraged him to be more proactive in coordinating weekend activities with the people he likes the most, but I think he’s afraid of rejection. I’ve also encouraged him to sign up for new or different sports/activities to make new/different friends, but I think he wants the kids he likes to like him better.

Whatever holds a kid back, it tends to improve with maturity, experience and the progression toward full freedom of movement that culminates in adulthood. Your boy has much young-adult exploration and self-sorting opportunity ahead, especially after high school — though high school, too, offers incremental improvement as elective paths open up. Even summer jobs crack the door to self-expression the way geometry class never will.

The sigh of relief is almost audible as less-well-adapted kids start to see a bigger pool of potential friends and occupations.
That, in turn, lets you stay out of it and focus on the family side of providing him with a meaningful, fulfilling and connected childhood. He’s sharing how he feels, so be there to listen, not fix things for him. Show interest in his interests. Learn to ask him good questions. (Good social modeling for him regardless.) Be the place he feels loved when he’s hurt. Have family field-trip plans handy, if he needs to be conveniently out of town sometimes.

In general: Watch for signs of serious distress, yes, but also let yourself appreciate the bigger story of the person he’s becoming.