If you look at this NGram, you might think that usage of "the day began" is quite common. If you look at individual usages, though, the story is quite different: most do not have the meaning that you are looking for. Here are some examples:
There is no question that in the calendar used in the Pentateuch the day began with the sunrise.
the great battle of the day began about noon
when the day began to wear away...
Looking at actual usages of the day opened, a much greater proportion relate to the start of the day (dawn) or to the start of activities on that day. They usually concern either the weather or military matters, or in this case both:
The day opened out with a very hot sun, and no firing was heard on the lines, nor shells from the mortars
Based on this, I think that the day opened is the more appropriate usage for a description of military activities.