Supposedly, Kal-El from the Man of Steel movie landed in and grew up in a Smallville-esque area in Japan where he is adopted by Japanese MHAverse counterparts of Martha and Jonathan Kent, who are both quirkless. The Smallville-esque town/village he grows up in is a place where most of the population is quirkless, the only quirks there being either completely useless, like an extra limb, or completely insignificant to be considered fit to pursue either heroism or villainy; therefore, the regulatory law regarding the usage of quirks here not as strict as compared to the more urbanized areas of Japan. Or any law for that matter. Nonetheless, Martha and Jonathan keep Kal's origin a secret from everyone and raises him on their own.
As the years pass by, under the influence of a yellow sun, Kal develops his powers as he does in the movie. People notice this but aren't afraid of him as they would be in the DCEU since, after all, super powers are the norm in their world. Kal knows about the existence of quirks and uses his powers to help people in his area whenever he can during his teenage years. This makes him somewhat of a local vigilante, but with the quirk law in Smallville being as lenient as it is, he doesn't get as much the negative attention from authorities as he would've in other parts of the country, making him getting away from most of it. Hero Academias aren't a thing in their area of the countryside and neither could Kal and his parents afford sending him to one, therefore making Kal go to a normal school from elementary till he graduated high school. By that time, he has developed most of his powers bar flight which he would attain at adulthood.
Timeskip brings Kal to adulthood, graduating from a journalism course(?) and now a journalist moving on to greener pastures in the city of heroes, Tokyo. There he gets a hired in a famous newspaper publisher as he does in the movie and plays out as it does in the movie. With Kal aware of the stricter regulatory quirk laws in place, he doesn't frequent being a vigilante as he did during his youth but still uses his gifts when he can to help people (discreetely, of course). He also idolizes the heroes who protect not only the city, but the entirety of the populace of Japan as well; particularly the Symbol of Peace and current Number one hero, All Might, making him wish he had gone to a hero school back in his high school days. From then on, things play on as it did in the movie and the anime up until the Kryptonian invasion, where Kal learns more about his past and takes on the mantle of Superman, complete with his blue and red costume and the giant insignia on his chest. (Important thing to note: The Kryptonian invasion occurs after All Might's final showdown with All for One, so he probably won't be of much help during the war)
Post-invasion, half of Tokyo is obliterated from Supe's battle with Zod and the whole world knows of his alien origins. Taking into account all of these events and with him existing in world where super powers are the norm, could Superman achieve or surpass what All Might did, as a Symbol of Peace, or in Kal's case, as a symbol of Hope? Or will the fear of the populace lead to his downfall?