Georgie and Mandy's Young Sheldon relationship was supposed to only be a brief fling, but after they accidentally got pregnant, Mandy became an integral part of the show. Since Mandy and Georgie are now engaged to be married, it's odd that Sheldon never mentioned her in The Big Bang Theory. If their wedding pushes through, however, it's worth noting that the socially inept genius referenced his brother's first wife, who would be Mandy. In any case, Sheldon's falling out with Georgie could explain why he never talked about Mandy in early seasons of The Big Bang Theory.
Georgie and Mandy's unexpected pregnancy brought grief and difficulties to the Coopers, with Mary even getting shunned from her church. All their hardships were wiped out, however, once Mandy gave birth to Baby Cece in Young Sheldon season 6. Named after Meemaw, she is George and Mary's first grandchild, which should be a big deal for Sheldon in The Big Bang Theory, considering that he even went home to help deliver Missy's first baby. However, just like Mandy, it's likely that Sheldon didn't have any connection with Cece during the early years of The Big Bang Theory because of his conflict with his brother.
In Young Sheldon season 2, it introduced Sheldon's fellow child prodigy, Paige Swanson. While she has never become a series regular, the comedy brings her back every season, allowing the show to continuously craft her own arc. Due to the divorce of her parents, Paige has dropped out of school and is rebelling. Her future fate remains uncertain, but considering how Sheldon and Missy have been tied to his narrative, it's curious why she wasn't mentioned in The Big Bang Theory. Sheldon may have simply opted not to talk about her because of their childhood rivalry. Otherwise, it could also be because Paige's story ends on a dark note.
Mary's church is deemed the true villain of Young Sheldon, which became clear in season 6. Led by Pastor Jeff, the congregation was a big part of the Coopers' lives until they were shunned away. Even when they have stopped going to church, Pastor Jeff continues to have ties with them because he is their neighbor. Between that and his help to Sheldon's Germany trip, one would assume that he would come up during one of the Pasadena gang's discussions, but that never happened. Considering Mary's return to church resulted in her becoming more judgemental, Sheldon may have opted not to discuss Pastor Jeff in TBBT.
As Sheldon's first mentor, Dr. Sturgis is the reason why the socially inept genius pursued theoretical physics, which not only became his specialization in Caltech, but also the field he won for his Nobel Prize. As seen in Young Sheldon, the pair has a great dynamic. Aside from that, the seasoned educator was also linked once to Meemaw, so it's puzzling that he never brought up Dr. Sturgis to his Pasadena friends, especially when talking about their work. Unless they have a falling out, it's simply unbelievable that not one time did Sheldon even refer to his original mentor.
While Sheldon sees Dr. Linkletter as another mentor, his relationship with the East Texas Tech professor is far from what he has with Dr. Sturgis. Still, Sheldon has worked closely with Dr. Linkletter ever since he started college, tackling various projects. However, the pair's conflict in Young Sheldon season 6 about Sheldon's grant database could be his reason for never talking about Dr. Sturgis in The Big Bang Theory.
After breaking up with Dr. Sturgis, Meemaw started seeing Dale. Their relationship has been tumultuous the last few years, but in the Young Sheldon season 6 finale, they seem to still be together. Aside from that, both Georgie and George also worked in his shop for extra income. That being said, The Big Bang Theory ignoring him shouldn't be that big of a deal. While Meemaw and other members of the family regularly interact with him. Sheldon barely crosses paths with him.
Sheldon talked about Billy Sparks in The Big Bang Theory, albeit his recollection of the character is inconsistent with what is shown in Young Sheldon. However, the nerd-centric sitcom never name-dropped his mother, Brenda. Considering her proximity to the Coopers, not to mention his relationship with his parents, she should have at least been mentioned in The Big Bang Theory at least once. Granted that Sheldon never really interacts with him, Mary could have brought her up during one of her many visits to Pasadena.
Introduced in Young Sheldon season 5, Rob started as the new Youth Pastor at Mary's church. His initial interactions were mostly with Missy and Sheldon. However, the show's storytelling shifted to developing a potential romance between him and Mary. While his appearances have been limited, Rob's complex relationship with Mary is still one of the biggest unaddressed plots in the prequel. Since Sheldon is oblivious to how Rob's existence has impacted his parents' relationship in Young Sheldon, he didn't have any reason to talk about him in The Big Bang Theory, and it's more unlikely that Mary would bring him up.
Sheldon doesn't really have any great relationships at East Texas Tech aside from the one he has with Dr. Sturgis. Despite regularly interacting with the school's president, Linda Hagemeyer, he never mentioned him in The Big Bang Theory. There are several possible reasons for this. Firstly, Sheldon didn't want his adult friends to know about his college days — something that he never really discussed in the mothership series anyway. Since he only knows Haegemeyer through East Texas Tech, it's understandable that he didn't talk about her. Secondly, she also tried sabotaging Sheldon's grant database in Young Sheldon season 6, and he didn't really like discussing his failures.