The Many Loves of Dobie Gillis (1959)

S2E30 Like Father, Like Son, Like Trouble

Title: Trouble Runs in the Family Plot: Dobie lands a role in a military-themed play, and while dressed in his uniform, he accidentally convinces the daughter of an army officer that he is an actual soldier. The misunderstanding leads to a series of amusing situations as Dobie struggles to maintain the charade while navigating his feelings for her, all while trying to avoid getting caught in the deception.