Nezuko was born as a girl named Ava, to a mother named Nova Amano. She knew from the moment she was truly conscious that she was a demon once more. With her claw-like nails, pink eyes, slit pupils, sharp teeth, vine-like birthmarks, and the orange ends on her hair, it wasn't the most difficult conclusion.
At 2 months old (when most babies start to babble) she said her first word, "Kaa-san." Since Nova, being the legendary weeb she is, learned Japanese when she was younger, so she recognized the word as "mother". Nova resigned herself to having the most unusual child on the planet.
At 3 years old, Nezuko had a decent grasp on the English language; then turned her focus to history, math, and science. She was considered a genius.
At age 4, she met her arrogant uncle, Tony Stark. Apparently he's a big weapons manufacturer. Nezuko didn't like him. But Kaa-san would leave Nezuko with him when she went on business trips, so they learned to tolerate each other.
The first 2 times trouble came knocking at her uncle's door, she was with Kaa-san.
The third time, Nezuko wasn't that lucky.