The official descriptions says that Supergirl arrives on Earth when she was about 12 years of age.
“She was sent from her dying home planet of Krypton to Earth, where she was taken in by the Danvers, a foster family who taught her to be careful with her extraordinary powers. After repressing said skills for more than a decade, Kara is forced to bust out her super moves in public during an unexpected disaster. Energized by her heroism for the first time in her life, she begins embracing her abilities in the name of helping the people of her city, earning herself a super moniker along the way.”
In the show, Supergirl will be a 24 years old woman.
Furthermore, another major role was announced by CBS. The studio is looking for an actress that would portray,
“26-year-old Alexandra “Alex” Danvers, Kara’s gorgeous, brilliant, science-minded foster sister. Growing up, Alex was partly jealous of her sibling yet also fascinated by her abilities, prompting Alex to learn as much as she could about alien anthropology, sociology and culture. Today, Alex works for a secret government organization and, alongside her heroic sis, will face many challenges, both mundane and super.”