Darth Sidious is one of the most notorious Sith in all of Star Wars lore, but even before he became a Sith, he and his master, Darth Plagueis, were both murderous children. They did not need Sith teachings to use their natural Force talents for their own selfish ends. Even without training or knowledge of what it was, they could feel the pull of the Dark Side, and they readily acted on it.
This is why Jedi have to begin their training so early in life, because it does not take long for human nature to take over. Without proper training in the light, people tend to turn toward darkness in the Star Wars universe.
In canon, little is known about Darth Plagueis' backstory, but in James Luceno’s Legends novel, Darth Plagueis, his public visage was Hego Damask, a Munn banker for the InterGalactic Banking Clan. Before Plagueis was born on Mygeeto, the Sith Lord Darth Tenebrous commanded his disciple to seduce a particular individual and bear a child. Tenebrous had foreseen that the child was going to be powerful in the Force, and he was right. That child became Darth Plagueis.
Hego was no ordinary child. Because of his uniquely planned conception, he was exceptionally talented in the Force. His mother wanted to cultivate that potential, buts she did not teach him about the Sith from the beginning. First, she observed and documented as his friends began to become “playthings rather than playmates.” On one particular occasion, a Munn child, whom Hego did not care for, tried to push past him on the stairs: “Grabbing his peer by the upper arm, Hego said, ‘If you’re in such a rush to get downstairs, then jump out the window.’ Locking glances, Hego repeated the suggestion, and his victim took it to heart. Many questions were asked after the youngling’s broken body was discovered in the courtyard.”
As for Darth Sidious, he was born Sheev Palpatine and was part of Naboo’s aristocracy. Even as an infant, his father, Cosinga, knew that Palpatine was oddly powerful and different from his other children. As a child, Palpatine also knew that he was special, and he maintained an attitude of ambition throughout his younger years. He was never pleased with his family’s station in politics and was constantly lobbying for more influence. His father, however, was content, and Palpatine despised him for it. Because Cosinga could not understand his son, he only pushed Palpatine away and tried to control him. Consequently, the two never really connected and even as a child, Palpatine secretly harbored a desire to kill his father.
Luceno’s Darth Plagueis novel goes on to explain that when Palpatine was seventeen, he befriended the banker Hego Damask, aka Darth Plagueis. Because of the monetary influence that Damask held, Cosinga did not like how their friendship boded for Naboo’s politics. Neither of them were aware of Damask's connection to the Force. Even still, Cosinga tried to restrict his son’s movements, and Palpatine snapped. Without even knowing what it was, he embraced the Dark Side. Palpatine murdered his entire family and their guards because he was tired of being limited by such complacent and controlling people. Afterward, he called himself “the king of beasts.”
Plagueis and Sidious both became murderous Sith lords, but these events demonstrate that even before they learned about the Sith, they were already murderous as children. This also shows how human nature often works in Star Wars. Without overt training in the Light Side, people will normally revert to a primal state and be inclined toward selfishness and domination. That is why the Sith are not worried about training children. All they have to do is find someone incensed by life and channel that anger into using the power of the Dark Side.