I served in the Greek army. No idea about the German army.
The first time you get a loaded gun (gun and a sealed magazine/clip) and you are without supervision, is when you start going on patrol or guard duty. Even on patrol, you won't be alone, so what's left is when you are on guard duty.
That was about a month into training.
When I was standing guard at night I had an mp3 player and I listened to music/radio or read a book. If I wanted to CTB, all I had to do was take the seal of the clip, load the rifle and shoot.
Except for the intense exercising, I hated the army. I was at armored vehicles division so spent most of my time at a garage, repairing or cleaning tanks.
Its not like you get your own personal firearm once you join the military, and even once you get a gun, what are you gonna do? shoot yourself in the middle of training? Probably smarter to look for another option or find something else you want to do
Even during training, you don't actually run around with a loaded gun. You do a move/manouvre and once you reach the designated spot, there's a clip waiting for you, you load it, empty it at a target, throw it out, an officer checks that the chamber is empty and you continue towards the next spot.
Generally, it would have been very difficult to CTB during training/exercise. Maybe hugging a hand grenade instead of throwing it would be the easiest, but you'd probably injure the ppl around you, so.... bad idea.
Actually, the most common way ppl CTBd was by stealing a couple of bullets during training and shooting themselves at their free time. Which is very strange since when you are on guard duty you have a whole magazine in your pocket.