Alsarah was born in Khartoum, Sudan. Both her parents are human rights activists. When she was eight, her family fled the country during the 1989 coup by future president Omar al-Bashir to avoid being killed as dissidents. They then lived in Taez, Yemen, before fleeing again due to the country's 1994 civil war. They subsequently arrived in the United States claiming political asylum and settled in Boston. During this turbulent period, she often found solace in music, listening to bootleg recordings in Yemen and taking casual piano lessons from a family friend.