Requirement 1: Spare Commander Seiji
The Assassin’s Creed Shadows Koshiro romance won’t happen until much later in the campaign, but you do meet this fella as part of the arc where you’re hunting for The Ox. Specifically, there’s a section where you have to join Koshiro’s search for his old pal, Seiji. Once you discover Commander Seiji’s location, you’ll see that Koshiro is already fighting him.
Join the fray and, once Seiji has been defeated, choose to spare him instead of killing him. This shows Koshiro that you value lives and that you’re willing to give people a second chance.