An was born in 1906. An's father was Tuyển (Trung Thành) and her mother was Huệ thị Vũ. Her paternal grandparents were Thuận and Vẽn thị Nguyễn. She had two brothers named Lai and Dương. She was the second oldest of the three children. She had two half-brothers and a half-sister, named Vũ, Cao and Nhàn.