No, Cupid has not always been depicted a baby. Originally, Cupid was shown to be a youthful young man, not a baby and was often portrayed as having a wife.
In ancient Greek mythology, Cupid was known as Eros, the God of love, and he is first mentioned by the author Hesiod around 700 B.C. In these original stories, Eros is a young man armed with a bow and quiver of arrows. Eros used golden arrows to incite love and desire while leaden arrows were used to incite aggression and aversion. Eros was said to enjoy meddling in the love lives of the Gods by making them fall in love with mortals or with each other.
The stories of Eros were retold by the Romans, and according to Roman tradition, Cupid was the physical embodiment of desire. By the time the Hellenistic age began in 323 B.C., Eros was being portrayed as a mischievous and meddlesome young boy. During the Renaissance, it became popular for artists to paint winged cherubs as a symbol of love and innocence. Eros, now only being referred to as Cupid, got swept up in the popularity of the winged cherubs; henceforth, he was portrayed as the familiar chubby baby facade.