Billings was born in Pembury, Kent and grew up on his family's farm in north Kent. He developed as a good all-round sportsman, playing tennis for Kent and being offered a trial for Tottenham Hotspur Football Club after scoring a hat-trick against the team's academy side whilst playing for Corinthian under-14s. He also played racquets, squash and rugby. His grandfather, Ron Billings, was a racquets champion and his cousin, Tom Billings, is a world ranked player of the game. Billings attributes racquets with helping to develop his batting skills, in particular his hand-eye coordination.

Billings attended Haileybury College in Hertfordshire, appearing regularly for their cricket First XI throughout his school career. He studied for a degree in Sport and Exercise Science at Loughborough University. Billings has said that he was "nowhere near good enough" to become a professional cricketer before his time at university and credits it with encouraging him to work hard to develop his talent.

Billings made his first-class debut for Loughborough MCCU against Northamptonshire in 2011. He made a further first-class appearance for the team in 2011, against Leicestershire. In his four first-class matches for Loughborough MCCU, he scored 321 runs at an average of 45.85, with a high score of 131. This score came in his debut match against Northamptonshire.

Whilst at university Billings was also a member of the Kent squad, and he made his debut for the county in May 2011 in a first-class match against his university side, Loughborough MCCU. During the 2011 season he also made his List A debut for Kent against the Netherlands in the 2011 Clydesdale Bank 40, standing in for regular wicket-keeper Geraint Jones. Billings made three further List A appearances in the 2011 season, as well as playing in fou