At some point he was homeless in the streets of Ashfield, sleeping in the passage of the South Ashfield Train station in a sleeping bag and trying not to starve or freeze to death.
When he was sixteen, a five-year-old Eileen Galvin approached him despite her mother's warnings. She gave him her doll out of sympathy before leaving with her mother. The encounter caused Walter to cry uncontrollably - Eileen was the only person to be kind to him and show him any sort of care. He treasured the doll she gave him, keeping it even in death.
At eighteen, he attempts to approach a girl he had frequently seen and watched in the train station, a thirteen year old Cynthia Velasquez. He stuttered as he attempted to make small talk and ask her about the apartment building he was born in. Her friends were dismissive and she called him 'handsome but filthy.' When he accidentally revealed he had known her name for years, she called him disgusting and immediately left with her friends.
This same year, he formally leaves Wish House as a young adult.
Headcanon
While technically still in the Wish House's 'care', Walter had all but run away at fifteen years old. He ended up returning to the Wish House a year later and was heavily punished for running away.
Walter begged and panhandled for money but was largely ignored.
During this time, Valtiel continued to haunt Walter and taint his worldview.
Adolescence
Canon