Josh Shigaraki was born in California, USA to a man who went by the name Taketo Shigaraki and a woman named Sarah Vallen. Sarah Vallen came from a well off business family while Taketo was seen as from a rich Japanese family. Soon after meeting Sarah and Taketo would get married and Sarah would conceive a child. Taketo Shigaraki quickly ended the relationship but would monthly head back to the U.S. to check up on the young child. Sarah Vallen had a quirk called Copy Gaze, a quirk that allows the user to copy somebody's quirk by making eye contact and the user stops being able to copy the quirk when they lose sight of the target. This was a bit strange considering most of the Vallen family's quirks were light based. Taketo Shigaraki was said to have the quirk Air Walk which allowed the person to walk on air.
During the monthly visits to Josh, Taketo would often ask about his quirk. He had yet to manifest one by the time he was 4. This started to worry Taketo. At first Taketo started to come over more frequently. About three times a month Then once it seemed like he wouldn't develop it slowed down to about once every two months. Finally, it came to the point he didn't visit at all for 3 months. During that time Josh's grandfather became gravely ill. At this point Josh was six. Taketo visited seemingly to help Josh through the situation emotionally.
6 days after Taketo arrived he stared at Josh asking if he would ever develop a quirk in a stern voice. A terrible voice. A voice not filled with rage, but with the utmost pity. A voice that whispers into your ear, you're a failure. That voice would haunt Josh forever. Those words were supposed to be heard by none other than Josh, but his grandfather overheard and was greatly disturbed by Taketo's words. That evening as Josh lay beside his grandfather his grandfather wished more than anything to give Josh his quirk as he wanted Taketo to love his son. At that moment Josh's quirk activated. And he took his grandfather's quirk, Luminescent Hands. This quirk allows one to generate light out of their hands. Josh's grandfather died within the hour.
Taketo soon found out about this before any of the family. Taketo took Josh aside and soon revealed his true identity. He was the villain All for One and his goal was to produce an heir capable of having the same quirk or similar quirk to use against One for All. Josh was that chosen heir. All for One gave strict orders to Josh. He was to tell no one of All for One's true identity. Secondly he was to never receive another's quirk without All for One's permission. In return he would leave Josh's family alive and train him up. Some quirk All for One had scared Josh into accepting the deal.
All for One then took the quirk Josh received from his grandfather saying, "You shall have nothing I don't give you. Now for your first test go and take your mother's quirk."
Josh hesitantly went to follow his father's orders but quickly discovered the limits of his quirk. His quirk called Choice of All only allows him to take other's quirks with their consent. It also puts great strain on him to receive a quirk. He soon returned to his father explaining he had failed.
All for One simply said, " No matter, your mother can keep her quirk. It was simply a test to see the limits of your power."
All Josh could do is nod. At such a young age any love he had for his father had turned to fear.
All for one continued saying, " I will give you a powerful quirk called Willed Weapons. It grants you the ability to create weapons out of thin air. Those weapons will be near indestructible being as powerful as your will. You can create normal objects like a table but they would be of no use to you because as soon as they leave your hands they will disappear. The same is with ranged weapons like a bow or gun. As soon as the ammo stops touching the main part it will disappear."
Josh did not know this at the time but the quirk Willed Weapon was actually three quirks in one. The basis of the quirk allowed the user to create objects out of light. Those objects were weak though and easily destroyed. The second quirk allowed the user to make any non-living thing they stay in contact with as indestructible as their will. The last quirk was actually Josh's grandfather's quirk which was more of an insurance to make sure Josh could always summon his weapons.
All for One soon left, but would make daily phone calls to Josh. He instructed him to learn Japanese as well as many other languages and to train in fighting techniques. Josh trained like this for 6 years until the age of 12. All for One came under the alias Taketo on Josh's birthday and asked Josh's mom to allow Josh to live in Japan with him. Sarah agreed as long as Josh made frequent calls to her and came over during school breaks.
Josh soon left for Japan. All for One told Josh that while in Japan he would go by the name Kazuaki, referencing his quirk. His name was supposed to mean all consent. His name in Japan was now Kazuaki Shigaraki.