Sam, if you are friends with them outside of social media, then why don't you try and set something up with them instead of waiting for them to invite you? If you're trying to compete with Facebook, SnapChat, Instagram, etc., you're going to have an uphill battle.
My son plays Frisbee golf, basketball, coaches basketball at the Y, etc. So he has lots of interests outside of social media. He'll start texting his friends saying he's going to be at this park at 6pm for a basketball game if anyone is interested. Sometimes he'll get as many as 15 people show up.
Get a hobby, join a book club, have your own interests that make your life fun. If this particular group of friends continue to exclude you, then use your hobbies to form new friendships. Good luck.