In real life, Phylicia Rashad (or Phylicia Ayers-Allen, as she was known at the time) was about 36 years old when The Cosby Show debuted in September 1984. While Clair's age I don't think is established, we do know that she's the mother of a 16 year old daughter Denise (Lisa Bonet turned 17 in November 1984), 14 year old son Theo (Malcolm-Jamal Warner was actually 14 also), 11 year old daughter Vanessa (Tempestt Bledsoe was also actually 11 in real life), 5 year old daughter Rudy (Keisha Knight Pulliam was also 5). Later in the first season, the show added 20 year old daughter Sondra, played by 26 year old Sabrina Le Beauf. So in a nutshell, Phylicia was playing mother to actresses that were only 10 and 19 years younger than herself.

Phylicia was in real life, 40 years old when on the show, she became a grandmother after Sondra gave birth to twins. Keep in mind that at that time in real life, she was the mother of a 15 year old son and 2 year old daughter. Granted, I want to say that it was later said that Clair was born in 1943, thus making her about five years older than what Phylicia Rashad was in real life.

But still, to put things into the proper perspective, if Clair was 41 years old at the start of The Cosby Show and her oldest child in the household, was 16, then wouldn't that mean that she was pregnant with Denise when she was still in law school? This is of course, assuming that assuming that Clair graduated from high school at the age of 18, graduated from college at the age of 22, and then started law school right after college.

And taking Sondra into account, wouldn't that also mean that Clair was pregnant with her while she was still in college?

Cliff and Clair if I'm not mistaken, originally said to be high school sweethearts and Cliff went to Hillman because of Clair. But later in the show's run, it's stated that Cliff was four years older than Clair (in real life, Bill Cosby is eleven years older than Phylicia Rashad).

In the fictional world of The Cosby Show, Clair Huxtable’s age was slightly higher than actress Phylicia Rashad's real age to make the family timeline more plausible.

Clair’s Canon Age

Birth Date: According to character biographies, Clair was born on March 20, 1943.

Age at Premiere: When the show debuted in September 1984, Clair was meant to be 41 years old. In contrast, Phylicia Rashad was only 36 at the time.

Age Milestone: In the Season 5 episode "Birthday Blues" (1989), the family celebrates Clair's 46th birthday.

The Sondra "Plot Hole"
You correctly identified a timeline issue caused by the late addition of the eldest daughter, Sondra.

Timeline Conflict: Sondra was born in April 1964. If Clair was born in 1943, she would have been 21 years old when she had Sondra.

Educational Impossibility: The show established that Cliff and Clair married after they both graduated from Hillman College. If Clair was born in 1943, she would have graduated around age 22 (1965).

The Result: This means Clair would have had to be a college junior or senior when Sondra was born, contradicting the "married after graduation" backstory.

Age Gaps with Other Cast Members

Sondra (Sabrina Le Beauf): Rashad is only 10 years older than the actress who played her eldest daughter.
Clair’s Mother (Ethel Ayler): The actress playing Clair's mother was only 14 years older than Rashad in real life.
Cliff (Bill Cosby): While the characters are close in age, the show gave contradictory info; one episode suggested Clair was six years younger than Cliff, while another said four years.