There's an issue with Sheldon's age, and it isn't that the show hasn't established when he was born. Rather, the problem is that it has established when he was born, but also contradicts that date.
It was referenced multiple times that Sheldon and his twin sister Missy were born on February 26, 1980. However, as Reddit user dgiannak discovered, the math of Sheldon's various life accomplishments doesn't quite add up, if one examines Sheldon's own accounting of his past in the first season episode "The Luminous Fish Effect." After he gets fired from his job, Sheldon declares he's not interested in getting it back, saying, "I've spent the last three and a half years staring at grease boards full of equations. Before that, I spent four years working on my thesis. Before that, I was in college, and before that, I was in the fifth grade."
Now, another established fact is that Sheldon, being the difficult genius he is, started college when he was eleven years old — something that is a major plot point on Young Sheldon. However, dgiannak notes that when that timeline is added up — four years for college, four for his PhD thesis, and three and a half working before the beginning of the series — that puts his age in "The Luminous Fish Effect" at only 22. That's about five years shy of how old he should be, at that point, which is 27.
This timeline fumble is likely nothing more than the result of a goof in the script. But it's also not the first time the show has had trouble pinning down exactly when Sheldon was born.
