HoMM3 HD is a mod (add-on) for the game Heroes of Might and Magic 3.

Here's the thing. There's no way to get the game start date from the save file.
However, the save file does store the map name. It's possible to extract the start date from the map itself, but if the map hasn't been saved or has been overwritten, that's a problem.

So, we also need to change the naming of random maps, writing the creation date and time instead of the number. Then the date and time will also be in the save file.

And then, a simple, universal option would be [map name]\112.gm2, as it would also work for offline single-player.