Born in 1988 in Turlock, California, Costa grew up in nearby Hilmar, California. He attended Hilmar High School, where he played quarterback for the football team. As a junior, he had 2,200 yards and 24 touchdowns through the air while rushing for 700 yards and six touchdowns. In his senior year, Costa threw for 2,252 yards and 15 touchdowns, and rushed for 1,709 yards and 18 touchdowns, for a total of 33 touchdowns and 3,961 yards of total offense. He received all-state honors for three consecutive years, and as a senior was selected as the Central Valley player of the year.