found the milk (and then a home) by MarryMoonlights

link https://archiveofourown.org/works/519...

“Daddy, I found the milk!”

The words were accompanied by a tug on his sleeve, and Hizashi startled so badly he dropped the tub of ice cream he was holding.

He managed to awkwardly catch it between his hip and the freezer door before it hit the ground, and let out a sigh of relief. Then he remembered his priorities, and glanced over to the right, where a young boy with bright green eyes and hair was nervously shuffling his feet, holding out a carton of milk with the hand not attached to Hizashi’s sleeve. He was tiny. Only four years old, perhaps? Five?

Hizashi looked in confusion from the hand on his sleeve to the milk and back to the boy’s face. “Hey kid, I think you’ve got the wrong—”

“No, Daddy, we always have this milk!” the boy said quickly, rushing the words before Hizashi could finish. This time, however, his eyes darted nervously over his shoulder, and Hizashi paused. That wasn’t just nervousness in the boy’s eyes – it was fear

Or: Hizashi saves tiny Izuku in a grocery store, and then proceeds to save him forever.