Disclaimer: I do not own Baccano!, and, by extension, any characters, events, etc.
This story is speculation based off of information from the light novel translations and information available to me, the conditions of the time period and the psychology of the characters. I have tried to be as accurate as possible in the probable events. Speculation on Firo's mom (though there's virtually no information on her) just fascinates me, so that's where I'll start.
1913
These streets were no place for a woman. Dirt huddled in every crevice and provided the only carpet most of the area's resident's would ever know. Softness had no place in their lives. Knives gleamed in shaded alleys and children shouted as the hot sun beat down on their play. If it could be called playing, as they were fueled by the violence they experienced daily. Cops and robbers would sometimes explode into a beatdown while the kids with tamer games would creep away and cover their ears.
She wove her way through ragged carts and people as she wondered if it was foolish to walk about so openly with an infant. There were other mothers out and about, but they seemed to blend with the area. She reminded herself that this was her neighborhood now, and she would have to blend in, too. There was no way she could afford not to. Her family had made it clear she could expect no help from them. Her few friends... She was too ashamed to let them see her. All that was left to her was a world of strangers and shadow and her little boy. In some cruel twist of fate, her provider had been taken all she had was an utterly dependant creature to comfort her.
The daylight made the place less scary. She held her fidgeting baby closer and tried to suck some light from the sun. She could use some optimism. Even being employed, the specter of tomorrow was no friend. Little job security was available fro a young woman in menial factory work, especially one who had to snatch moments to feed a baby that her employers thought was born out of wedlock. Which made sense, as she'd regretfully followed her deceased husband's order to sell her wedding ring so their savings wouldn't evaporate too quickly.
There was still money, she reminded herself. He hadn't had much after fleeing Italy, but he'd found a job before he even met her. As the cancer creept through his lungs and was repeatedly dismissed as 'just another bad cold' he'd built up all he could. They'd expected a comfortable life as they married, but after the illness didn't fade, they visited a doctor and found the truth. By then, it had been too far along that even his best efforts to fight it were fruitless. He'd died before their child was even born and she went through labor alone, still a mourning wife.
There was still money, but even with scrimping back when she was too weak after the birth to work, a lot had gone. She'd moved into the cheapest neighborhood she could find and sold all she could, but it still wasn't enough. Just as bad, the struggle of balancing baby and job were already wearing her down. Sundays like these were the only times she could recharge.
But she was determined. She'd stared down her parents as they scowled at her soul mate and cast her away. As soon as she felt well enough, she'd scoured the city for a job, willing to take everything, and found one. It was horrible, in a place as dirty as her new neighborhood, with long hours and draining work. She'd stick through it, simply becuase it was necessity. Monotony and discomfort didn't matter anymore, they were her life. She would survive, at least until her little baby could on his own.