What idea started growing when Billie told bud that he didn't know who his daddy was?

When Billie told Bud that he didn't know who his daddy was, it sparked a growing realization in Bud about his own identity and the importance of family. This moment highlighted Bud's longing for connection and understanding of his roots, propelling him on a journey to discover his past. It also emphasized the theme of searching for belonging and the impact of parental relationships on one's sense of self.