In the very first shot of the movie, a clock is shown ticking. The time on the clock reads 05:59:56. It is obviously AM because a few seconds later at 06:00:00, Frank wakes up as if it was morning. As Frank sits up, clear daylight is visible outside of the window. This scene is supposed to be set during winter. We know this because there are many Christmas decorations. Since this is meant to be winter, it should still be dark at that time of day.
Frank Moses' file, seen when Cooper is told he is his next target, gives Frank's date of birth as March 19, 1955. This is Bruce Willis' date of birth.