Before the story starts, I want to say I changed part of Izuku's quirk definition. Instead of the quirk sticking with him, he can choose to get rid of it or not. And when he changes into an animal, it can aslo be a mythical creature.
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Quirks?
Four Years And Eight Months Old...
"Your quirk is so useless!" Kacchan said as he laughed and bullied a crying kid.
"Stop Kacchan! That's not nice!" Yelled Izuku as he stepped in front of the kid protecting them.
"Trying to play hero? I think a quirkless kid is way worse than a kid with a stupid quirk." Stated Kacchan. He and his goons slowly steped forward, attaking Izuku.
Izuku went home with many burns and bruises that day.
Four Years And Nine Months Old...
Izuku sat in his room crying on his bed. He wish he had a quirk. Then maybe him and Kacchan would still be friends. Maybe hos dad wouldn't have left. Maybe... He could be a hero.
'No. No, even if I don't have a quirk... I'll still be a hero!'
Four Years And Ten Months Old...
"Mom?"
"M-mom... are you, okay?" Izuku asked again.
"I'm fine, Izu. Go back to bed, okay?" She said.
"O-okay m-mom..." He answered.
Four Years And Eleven Months Old...
'...'
'Why. Why did I have to be the unlucky one. The quirkless one...'
Izuku's Fifth Birthday...
Izuku sat on the couch, watching T.V. while his mom made his favorite meal, Katsudon, for his birthday.
How Izuku wished he could be luky on his birthday, and get a quirk. A cool one like telekinesis, so he could use the T.V. remote without getting up. Or he could help his mom cook. Or he could be a hero, and save people with a smile.
Or if he had a time quirk. He could stop time and make it to school on time after his beetings by Kacchan. And he could be a hero, stoping villians with time.
Or, maybe if he could teleport... That woupd help with getting to school on time. And he could also be a hero with that quirk.
Then the impossible happend. Just as Izuku looked at the T.V. remote, it started floating.
'Did I mummble again? Is mom trying to make me feel better?' Izuku thought. He then looked behind him, to see no one was there. It hit him like a train.
'Oh My God! I'm doing this! It's me!'
He looked back at the remote, and waved his hand, making the remote move side to side. It looked like it was dancing through the air.
'I wonder... This quirk came when I wished I had it... What if... I really wanna have a time quirk! One that let's me stop time!'
As soon as Izuku was done, he tested it out. To his surprise, he already new what to do and how to work it. All he had to do was say 'Time Freeze!' And the time would stop.
"Time Freeze!" Said Izuku. Everything around him turned black and white. He slowly got off the couch, and went to the Kitchen.
His mom stood there, frozen in time. So, he turned around and walked outside. It was the same. He saw the world black and white, everyone still frozen.
'Huh... This... This must stop the whole world! I mean, if one part of the world stops, then the rest would have to, too!'
Izuku walked back inside and sat back down on the couch.
"Time Continue!" He said. Everything went back to thier normal color, and things started moving again.
"If my quirk is what I think it is, then I can be a hero! But I want to try one more thing..." Izuku said to himself.
'Quirk teleportation! With this quirk I want to be able to teleport anywhere I want. No matter if I've been there or not.'
He then thought of where he wanted to teleport. And chose he would go to one of Hawaii's beaches, because he heard they were pretty.
"I want to go to a beach in Hawaii!" Izuku said as he closed his eyes. When he opened them, he was standing by the seashore, watching as the waves crashed into the sand. He looked up and saw a beatiful cloudless sky, and a rainbow going over the bright sun.
"No way..." He muttered to himself. He then relized that if he stayed any longer, his mom would relize he was gone, and would worry. With that, he said the words, "I wanna go back home," and left.
Back at home on his couch, Izuku released a sigh. He could do it. He could be a hero. He had a quirk. One even stronger than All Might's, at that.
"Izuku!" Inko called, "Dinner!"
Izuku ran into the small dining room, and sat at the table. His mom walked in hands full of food.
"Mom, allow me." Izuku said. He then used telekinesis to take the food out of his moms hands, and set it down on the table.
"I-Izuku... Y-You... G-Got your qu-quirk..." Inko staded, breath taken.
"I know mom! I was thinking about how cool it would be to have telekinesis quirk! Then I saw the remote floating. At first, I thought I had muttered and you had heard me. But, it turns out it was me!" The green haired boy said, "And that's not all! I thinky quirk is stronger than All Might's! That's why my quirk took so long to develope!"
"But, Izuku honey, a telekinesis quirk, it doesn't come close to the strength All Might has..."
"I know... But the telekinesis is only part of my quirk!" He said. Inko stared shocked, but nodded her head for him to continue.
"My quirk is that I can create quirks!" He told her. Sadly, it was a little to much to drop on her shoulders, and she fainted.