From Deku's perspective

Deku was teary-eyed, Bakugo had done it again. He retrieved his now burnt and soggy Hero Analysis for the Future No. 13 from the fountain. With his lip on the floor, he dragged his feet for the way home. Not having it in him to look forward, he didn't notice the sludge villain filling his lungs until it was too late. What do I do now?! I can't even breathe, he's too strong! Passing out, he hears without processing "Texas Smash!"

Waking up a little later with taps to the face, he jumps back in shock to see HIM! All Might! In the flesh! After fanboying, he tries asking him to sign his book. He's shocked to notice that he already had. Still having questions, he holds onto All Might's leg. Landing on the roof of a building, Deku is aghast to learn his lifelong idol's true form as well as his thoughts on him becoming a hero without a quirk. All Might leaves him to suffer this shock without getting further answers... nothing...

After processing to the point that he mentally has it in him to at the very least walk home, he does so. Passing a main road, he notices a large commotion. Looking at the source of it all, it's the sludge villain! That's the guy All Might captured! But how? ...

"Is that a civilian?" asked someone with a somewhat unsurprised voice out of peripheral view. Others confirmed his suspicions.

It was me, my fault! If I never interrupted him, this wouldn't be happening to whoever that poor civili- It's Kacchan! Seeing none of the heroes acting, his very being couldn't handle it. He raced forward! What am I doing?! Chucking his bag at the villain's face, he tried digging Kacchan out. Not really noticing until he felt an arm grab him!

Now in the POV of Saitama

Nothing good's on TV, maybe I should go for a walk. I'll bring the hero suit just in case. Saitama packed a bag and headed outside. To the park? Well, I could start there and just stroll the streets for a bit I guess. He didn't find anything of interest really. Not even petty villains to be stopped by the heroes who bother with that stuff. It's not like that never happened though. Then he noticed why the streets were quiet, there were explosions coming from a main road.

Rounding the corner, he saw a giant sludge villain and half a dozen heroes doing nothing. "Is that a civilian?" he asked 5% less nonchalantly than he usually was. Others confirmed his suspicions. So that's why they're not doing anything. Well I could try distract him, or just pull him out and hope there's only the one. At the same time as this wondering, he escaped view and changed into his hero suit. Emerging once more, he noticed some kid throwing his bag at the villain's face and try digging the other out of his slimy grasp. He distracted him, perfect! I can grab them both out of there. He did this with such speed that the wind blew people near off their feet! In the blink of an eye, he had them both dozens of meters from the villain. "Texas Smash!" resounded as All Might uppercut the villain so hard that clouds drew in and rain poured. "Huh, changed the weather." Saitama thought outloud as nonchalant as always... again.

"You-you saved us!" blurted the boy who dived in to save the other. He started to seem very sheepish while the blonde hair one yelled at him for saving him. Guess that bravery can only last so long. "And you too! I didn't need your help! I could get out there on my own!" the blonde one yelled. Is this kid really so stupid he didn't see how I helped?! How this guy helped?! "Hey pal, you should be thanking I us! Kissing our feet!" Saitama retaliated. After a little bit of bickering, and everyone leaving, All Might came and congratulated all 3 of them on their bravery. "You, what is your name son?" he asked Saitama. "Oh, I don't go by a name, don't really have one yet." Damnit, he's gonna ask me what's the name on my license! I can't tell him I don't have one and I'm a vigilante! I can't prove my power's not a quirk! But before he could ask, the green hair boy piped something up. "Excuse me sir, can I get a word with you?" Poking his index fingers and head to the ground to avoid eye contact he added, "Alone?" This seemed to disorientate All Might and he simply made the excuse of checking on the victim.

"Thanks kid, you saved me there."

"Sa-saved you?! Oh that reminds me!" With a deep bow, he accidentally yelled "My name is Izuku Midoriya! Thank you very much sir for rescuing me! I'm sorry I got caught in it all and made your job harder!"

"You're joking right? I probably still could've gotten that guy out of there, but you made it even easier. It was a smart move to throw your bag at him like that, it distracted him enough for both of us to act." The green haired boy was... starting to cry? Is this kid for real? The teen started babbling on about how brash the decision was and how irresponsible he was, and lucky that someone else saved him he was. "Okay kid, stop crying. For real, please." With sniffs, he looked up at him, tears slightly calming.

"I have to ask you something." This caught the bald man by surprise. "I don't have a quirk, I have nothing special. I don't know how to fight or anything, but I want with all my heart to be a hero. I was already told today by someone I admire that I can't. Do you think I could?" He could see the look in his eyes, beyond the still dwelling tears were pure passion and sincerity. "I don't think you're asking the right guy. The No. 1 hero is right there." Seeing the sadness come over him, he realised. "But in my opinion," got his attention enough to not focus on being sad, "whoever told you that is an asshole and shouldn't be listened to. They probably think they're better than everyone because their quirk is just so great. I wanna tell you something that might come as a surprise, but you gotta keep your trap shut about it."

Izuku's gaping mouth closes and he nods his head vigorously in response. "I don't actually have a quirk." This makes the boy's head spin, he wants to explode with the thoughts pouring into his mind, making himself hazy. He mutters for a while until Saitama intercepts, "I can train you." This is enough to completely shut Midoriya's mouth. "It's not a lot of rules, but break them even a little and I won't carry on helping your sorry ass!" The boy starts asking questions at such a quick-fire that it's impossible to answer. Questions about what sort of exercise there is, sleeping arrangements, how he'll fit in studying, diet and all to many topics. Saitama's eyebrows deeply furrow, making his serious face and a fist he screams "You need to learn to keep that mouth shut or I'm gonna punch you harder than All Might lunched that sludge villain!" Deku let out a squeak and nothing further. "Look, meet me at the park tomorrow at 8 o'clock sharp." He wanted to rant about that not being exceptionally early and if that was only for the beginning and a lot more, but fear still held his tongue. With that, the 2 split and wound home.

All Might never got to see Deku and tell him what a great hero he was, tell him how he could become a hero, or offer One For All... The next day at the park, 8am. From Deku's perspective.

Deku was ecstatic, it was his first day of training to make it into UA and one day become the greatest hero! And the first quirkless to do either no less! He made it to the park and saw his shiny-headed teacher there already. "Good, you didn't back down." He simply smiled at this. "Before we even begin, this is a last warning. I had no one there to push me to do this routine, but you can bet your ass I'm pushing you harder than I did myself! I did it for 3 years, you've got 10 months. Of course, you don't need nearly as much power as I have to get in, but you're gonna aim for it. Got that?" He stated demandingly. "Yes'sir! I'll push myself to be even better than you."

"That's a little much kid, but you'll need that enthusiasm to get a third of it. It's pretty simple, but don't let that make you think it's not completely serious. You need to do this every single day, Monday to Sunday, not a single off day. Get sick? Too bad. Break a leg? Too freaking bad!" Geez, this guy's intense. He can't be serious about breaking a leg, can he? "You'll do 100 sit-ups! 100 Pushups! 100 Sit-ups! 10km run! Every day!" He said with the same face and fist as the day before.

"Ho-how many sets...?" The boy said, lowering his face to hide it with his hair.

"One. That means you'll have to do each all in one go!"

"Oh, um, okay. Well, what about diet? And sleeping hours?"

"Do I look like your babysitter? You can eat whatever you want and sleep whenever you want, just be here everyday at 8am sharp."

"So literally nothing else? That's all you did and you don't have a quirk?"

"You can backchat after you've warmed up with your 10km run! The park's perimeter is 1, so ten laps! And I better see you running!" Izuku Midoriya started his training for the next 10 months screaming from being chased by his new mentor.

The rather quick time it took to train everyday left Izuku more than enough time to study. He didn't need to, but he also started eating much healthier and following diets to help muscle growth. With the spare time outside of all of this and sleeping, he spent learning the basics of fighting, like balance and form. He learned a few ways to punch and even kick. The 10 months had passed so quickly it seemed for the determined boy. It was the morning of the exam, but that didn't mean he was not going to train. "I gotta say kid, you've done really well." Saitama noted when the plain faced boy was grabbing his breath after the usual training. "For 10 months, you've pushed your body to new heights, and you didn't skip a single day's training. Honestly, I thought you would've taken at least a week's worth off, but here you are even on the day of the exam, training all the same."

"Well, like you said, the end goal is to be a hero, not just get into the school. But I still don't understand. I know your training regime now for months, but how did you really not know you wanna be a hero until you were in your 20's?"

"I'll tell you the story one day, but you should be going, don't wanna be late!" Deku nods with a smirk on. "Good luck." The smirk grows, and he goes off. This is it, today I become the first quirkless student to study and become a hero!

Just to clarify, this only adds Saitama to MHA and not a single other character. Even though season 2 of OPM isn't out, there's hints that there's more to his training, but not knowing it, I'm going with the fact that it will also work for Deku. In fact, I think it works well since very he doesn't use a quirk while doing this training.