This is an interesting article from the March 23, 1912 edition of
The Sporting Life which bears on the question of start times in general and the NY Giants in particular. It appears that some Giants fans were agitating for earlier start times - either 3:00 or 3:30. Owner John T. Brush favored the 4:00 start time, but decided to let the fans express their preference.
I haven't followed up this story to see how the voting went, but I'm fairly certain that the start times for Giants games remained at 4:00.