Greenville County Master Deputy Michael Hildebrand told WYFF-TV In Greenville that a package was found at a postal facility near Greenville between 2 and 3 a.m. on Oct. 15.
I would assume they mean it was processed between 2 and 3 a.m., and not that it arrived between 2 and 3 a.m.?
What you have is a statement that I take to mean that the letter was "found" in the early morning.
Mail Processing Facilities generally have something going on 24/7. The time of discovery is not otherwise meaningful.