My Hero Academia depicts a world where supernatural Quirks are the norm, and it could be said that "normal" people have been left behind. There's a stigma against Quirkless people, and no one knows that better than Izuku Midoriya. He longed to be a great hero like his idol All Might, and once he received One For All, his dream was unlocked.
But what would have happened if Izuku never received One For All? It is actually conceivable that Izuku's story arc could have been roughly similar to what it is now, even if he remained Quirkless. Already, a few characters in both the anime and the My Hero Academia Vigilantes manga series prove that Quirks haven't made everything else obsolete just yet.
Izuku's Quirkless Style
Could Izuku Midoriya really take on Quirk-enhanced villains and win? He just might. Of course, Izuku could not challenge the likes of All For One, the flame villain Dabi or the mobster Overhaul in this state; those villains require powerful Quirks to defeat. The good news is that many lesser villains are really just thugs with punkish clothes and minor Quirks, and a well-trained, Quirkless hero could turn the tables on them in a variety of ways. Izuku has what it takes.
To begin with, Izuku was always a smart kid, and he quickly compensated for his lack of a Quirk with his sharp observations. He kept a notebook to log everyone's Quirks (hero and villain) and study them, and he can deduce anyone's strengths and weaknesses even in the midst of combat. Many heroes and villains alike get carried away or overconfident in battle due to their Quirk, and a crafty opponent like Izuku can take advantage of that. All Quirks have drawbacks or blind spots, and Izuku is ready to spot them. If Izuku can dictate the terms of battle and ambush a villain, he may capture them before the villain's Quirk comes into play at all.
In addition, Izuku can reach peak physical condition (for his age) and use his agility and strength to his advantage. Some pro heroes, or aspiring heroes, are general martial artists with a thematic Quirk thrown in, such as Mashirao Ojiro. Aside from having a strong tail, Mashirao is an ordinary person, and if he can qualify for U.A.'s Class 1-A, it's conceivable that a Quirkless Izuku could serve as a vigilante or a pro hero with physical prowess alone.
Izuku Teaming Up With Pro Heroes
Not all pro heroes (or villains) operate alone. Some Quirks work best for duels, where a hero can beat down a villain on their own, and other Quirks work best in a support capacity. If Izuku has the wits, strength and resolve to be a hero despite lacking a Quirk, he can match other pro heroes in power if he's assigned one or two support heroes in his team. Already, a few characters in My Hero Academia stand out as fine candidates.
Shota Aizawa, or Eraserhead, is one such candidate. He has the Erasure Quirk, which will negate a person's Quirk upon visual contact, and that allows Eraserhead to use martial arts and tools to capture the villain without difficulty. If the villain's Quirk cannot be erased (which is often the case), Aizawa is effectively Quirkless, but that doesn't stop him from being a pro. If he teamed up with a Quirkless Izuku, the two of them can easily capture villains. If Aizawa uses his Erasure on numerous villains at once, then it's even more important that he has someone like Izuku on his team.
Momo Yaoyorozu of class 1-A would be another great partner for Izuku since her own combat prowess is somewhat limited (even though she can make weapons). She is a definitive support hero, and during a mission or patrol, she could craft just about anything Izuku would need to take down a villain, from handcuffs and combat shields to gas masks or tear gas grenades, among others.
Ms. Joke, a teacher at Ketsubutsu high school and a pro hero herself, could also back Izuku up. Her Quirk does no damage; instead, it forces her opponents to laugh hysterically and lose focus, which would make it easy for Izuku to restrain them until the police arrive to take them away.
It's true that the best heroes have mighty Quirks, such as Endeavor's Hellflame or Hawks' Fierce Wings, but not every villain is a doomsday threat, like the Nomu. Bank robbers and drug traders are everywhere, and even a Quirkless hero like Izuku can and should take them down. Let the big heroes take on the League of Villains -- a Quirkless Izuku could clean up the rest.