It is possible to select new and blank hero mode files in the file menu, allowing you to copy, delete, and see the starting in-game time, which is normally not possible. You can also use this to start a file without naming it. Note that the game will crash if you try to start up a blank normal mode file, so this is mainly intended for blank Hero Mode files.
First, start the file you wish to open. Then without ever saving the game, die. The fastest place to die is using the bridge post in front of the goddess statue. Once you die, select "Quit" on the Continue prompt.
You will return to the file menu and the file that you started will be opened. As you never saved, it is still empty as it was. You can see the current game time, so it is now possible to find the game time on a Hero Mode file by simply subtracting the start time from the end time. You can also press '+' to copy the file and '-' to delete the file, which is normally not possible with a blank Hero Mode file.
If you start a Hero Mode file by opening it in this way, you can play the game and save the file as "Hero Mode". Just select "Start" when you've opened the empty file and play the game normally.
Saving now will save all your progress, but the file will still say Hero Mode in the file selection screen, you'll get to pick a file name, and the intro cutscene will trigger, starting you in the Knight Academy with all your saved progress.