What time in the morning do Sunday newspapers come out?

Question

Specifically for San Antonio....

Answer 1

I can't speak specifically for San Antonio, but Sunday newspapers are printed during the early morning hours (roughly 2 a.m. to 5 a.m.).  Most large papers are distributed by about 6 a.m.  If you want to see one really early, most papers put some early copies in the box near their office, and get some early street sales.