If any character has a race/culture, every character does.* There is NO DEFAULT. Even if two characters are white, or black, they’re not from the same place, with different accents/dialects/languages, folk stories, and customs.
Give your character ONE aspect that is common or valued among your character’s culture. This is how the audience sees your character’s culture. Celebrate it. More than one aspect threatens stereotypicality.
Give your character one aspect that is uncommon/antithetical among your character’s culture. This is how your character stands out when surrounded by their childhood figures. It also reminds us that their people are not identical and their culture is rich in breadth.
*In a game where everyone comes from the same culture, think about your characters’ families. Even if we’re all German settlers in 1846 Fredericksburg TX, my family might be poorest, yours might be toy makers, his might be criminal, hers might be religious.