In truth, Alfred was young when Aethelwulf died. As was the practice of the day, Aethelwulf divided his kingdom between his two eldest sons. Aethelbald and Aerthelberht ruled Wessex and Kent respectfully. Upon his death Aethelberht inherited Wessex. He died and the kingdom passed to Aethelred who made his younger brother Alfred his heir despite having two sons. Upon Aethelreds death, Alfred became King.
Although Jennie Jaques portrays Alfred and Aethered's mother in the show, she is infact only ten years older than Ferdia Walsh-Peelo, and two years older than Darren Cahill.
Several problems with the way they show Alfred becoming King, aside from the fact it's not factual. 1. The English didn't practice the election of monarchs, that was something done for the Holy Roman Emperor. 2. A crown wasn't used in the coronation ceremony until Athelstan's, Alfred's grandson, in 924. 3. The ceremony itself wasn't put into it's current form until Edgar became King in 973.