She and her mom became wards of the Emperor Theodosius after the death of her father, Antigonus, a senator in Constantinople. Her dad left her quite well off, and Theodosius apparently took reasonable paternal care on her behalf, arranging marriage to a senator's son when she was five years old. Perhaps that sounds bad -- she wasn't expected to marry the boy then, but that's when the betrothal was inked.
She and her mom moved to the family estate in Alexandria, where her mom died. I'm not sure if Euphrasia moved into a convent before or after the death of her mother, but she spent the rest of her childhood in the convent.
When she turned twelve (childhood was over fast back then), the new Emperor, Aracdius, summoned her to enter her marriage. She asked his permission to remain at the convent, suggesting that he sell all her father's property and use the proceeds to aid the poor and purchase freedom for slaves.
Although she was in many ways a model nun, she was a foreigner and the Alexandrian women could be mean girls. She was subject to scurrilous gossip, but was eventually recognized for her exceptional holiness.