This is gonna be a little different from the game but as Japan lives underground since the bombings and survive after numerous attempts of monster attack. Izuku and the crew (+Momo) left due to Izuku and Momo finding a new place so they can call home but during the journey they met and help people along the way.

Ship

Izuku x Momo

Momo is a bit thicker then what she looks in the picture

The crew:
Loid (Marshall)
Izuku
Momo
Shoto
Saiko (medical staff that the found)
Eri(daughter of both Shoto and Saiko and niece of Izuku and Momo)
Katsuki
Kirishma