I'm watching Netflix's Rise of Empires Ottomans and they totally skip giving any context to why Mehmed's father (Murad II) simply retired to leave his 13 year old son in charge.
Murad made no formal proclamation on the subject, but according to Halal Inalcik, in his The Ottoman Empire: The Classical Age, Murad felt satisfied that he had guaranteed his state's borders via the Treaty of Yenisehir (1444), which ceded lands in Hamadili to the Karamanids of Anatolia. With that step taken, "and while still in good health, he abdicated in favour of his son Mehmed" – who was then 12, but would become Mehmed the Conqueror, the sultan who took Constantinople and destroyed the Byzantine Empire – "hoping thus to establish him securely on the throne." In other words, Murad seems to have hoped that his person, his experience and his prestige would guarantee a peaceful of transition of power in a way that might not happen had he taken his chances that disease or happenstance might not terminate his reign more suddenly.
Unfortunately for Murad, his enemies were unwilling to allow Mehmed time to adjust to the rigours of ruling the Ottomans, and both the Byzantines and the Pope took steps to encourage Hungary's "war party", under King Ladislas, to begin fresh hostilities. Mehmed II was too young and too new to the throne to have much chance of resisting adequately, and a power struggle resulted in which the Grand Vizier, Candari Halil, was pitted against two of the new sultans tutors. Murad was forced to return, and won the decisive Battle of Varna soon afterwards – "going into battle with the text of the broken treaty pinned to his standard", as Donald M. Nicol observes in The Last Centuries of Byzantium, 1261-1453. His victory, Inalcik judges, "sealed the fate of the Balkans and the Byzantine Empire."