The events of Young Sheldon explain why Sheldon was generous with his money to Penny in The Big Bang Theory. Despite ending up as best friends, Sheldon and Penny's relationship had a rocky start. Suffice to say, they wouldn't even have any ties to each other had it not been for Leonard who had a massive crush on their new neighbor. However, the fact that they are unlikely friends makes watching them develop that bond so much more special.
In the early seasons of The Big Bang Theory, Penny was a struggling wannabe actress who moved to Pasadena to fulfill her dreams. Unfortunately, she wasn't the best at dealing with her finances. Penny did become a Cheesecake Factory employee to support herself, but it still wasn't enough, especially since she had a penchant for shopping while remaining generous to her past boyfriends. At one point, she borrows money from Sheldon for her utilities in her apartment, and he surprisingly lent her cash without any strict conditions.
This was uncharacteristic of Sheldon, who used to be very selfish. It's also worth noting that this took place in the early years of The Big Bang Theory when the pair still hadn't fully established a strong friendship making this more interesting. Sheldon's surprising gesture could be explained by Young Sheldon. In the spin-off, George is often stressed by the possibility of not having enough money. While George is a good dad in Young Sheldon for the most part, his bad qualities tend to come out when it comes to financial matters as it stems from George’s fears of not being able to support his family. Sadly, this mentality has created several conflicts in the Cooper household. Seeing this, Sheldon was more willing to share his money with Penny, as he didn't want to be subjected to unnecessary drama.
Young Sheldon's Explanation Makes Sheldon & Penny's TBBT Story Better
Sheldon's decision to flippantly lend Penny money wasn't fully explained in The Big Bang Theory. Even their other friends were surprised that he was willing to give her money or that he even had extra cash lying around. This specific plotline was mainly done for comedic purposes. However, seeing Sheldon's childhood in Young Sheldon gives it much deeper meaning. The spin-off is often criticized for creating The Big Bang Theory plotholes with its storytelling. While not intentional, exploring Sheldon's life with his family in Texas inadvertently shines a different light on otherwise mundane happenings in Pasadena. Although he was still acting as if Penny was more of an annoyance to him at this point, the fact that he didn't want to have any conflict with her hints that he was always fond of her future best friend.
Arguably more than any other relationship in The Big Bang Theory, Sheldon and Penny's friendship was the most satisfying to watch develop over time. Perhaps Penny reminded Sheldon of Missy as both girls have a similar vibe and characteristics as seen in Young Sheldon. It's only a shame that they didn't get to interact more as Missy's The Big Bang Theory appearances were very limited.