There are a ton of different kinds of pistols, and all have varying types of trigger weight. If you trained in a EU military, you probably trained with something like a Beretta 92 or CZ 75, both of which have a double action/single action (“DA/SA”) design, where the long DA is a safety feature. After the first shot, the gun will be in SA mode, with a much lighter weight for easier follow-up shots. One can also put a DA/SA gun into SA mode by chambering a round and cocking the hammer. Most consider this to be an unsafe way to carry a pistol without a further manual safety (both the Beretta and CZ have one for carrying in this manner).
Glock is the most common pistol make in the US, and they use a striker fired design. A striker fired pistol is typically equipped with a medium-weight trigger - lighter than a DA pull, but not as light as a SA.
Because the toddler shot himself in the chest, he was also likely using his thumbs, rather than index finger on the trigger. I think a toddler would easily have the strength to pull a striker trigger, and definitely a SA.