Maybe Sasuke and Naruto have a conversation before Boruto's birth about what it means to be a father. Sasuke shares his own thoughts based on his family's past, and Naruto listens intently. This conversation deepens their understanding of each other and sets the stage for Sasuke to be more involved in Boruto's life as he grows up, as an uncle - like figure.
Sasuke could be present at the village during Boruto's birth. He stands as a silent protector, keeping an eye out for any potential threats while Naruto is with Hinata. This shows his loyalty to Naruto and the village, and also how their bond has evolved to the point where Sasuke is part of Naruto's family in a way.