Disclaimer: I obviously own nothing. This story is fanfiction. This disclaimer applies to all chapters of this story.
When you're born, you're born with the first words you'll ever say to your soulmate written on your body. No one at the orphanage or school could ever tell Tom what the words appearing on his left forearm meant, but he assumed it was either related to doing some sort of magic trick or something spoken in some language that wasn't English. Because of this, his interests as a child were guided heavily towards becoming a magician and learning other languages. He had no luck in learning what his words meant during his first 11 years of life.
When Tom learned he was a wizard, he was so excited to have it confirmed that he was special. It also let him know that his focus on looking towards magic tricks and other languages wasn't completely off the mark. Instead of telling Professor Dumbledore about how he could control animals and hurt people with his magic, he asked about his soulmark. The professor's facial expression darkened, and he told Tom that he was too young to know about the meaning of the words. This annoyed Tom endlessly, and once he became a student at Hogwarts, he spent most of his spare time in the library.
Tom, being a presumed muggleborn and a poor one at that with his second-hand school supplies, had nothing but free time to spend in the library outside of classes and homework. He wanted to learn about the meaning behind his soulmark and why it would upset someone. He also wanted to learn about his lineage and all he could about Hogwarts and the wizarding world.
He learned about his lineage during his 4th year as well as the meaning behind his soulmark. Learning that he was the heir of Salazar Slytherin, one of the founders of Hogwarts and the particular founder of the house he was sorted into, made Tom feel very proud and at ease with himself. Learning that the first words he would ever say to his soulmate were the killing curse, heavily implying he'd kill his soulmate upon first meeting them, filled him with despair. He became determined to never utter the killing curse. It was illegal after all anyway.
Deciding to never use the killing curse didn't last long. Not too long after Tom set the basilisk upon Hogwarts during his 5th year he learned about where his father was, and he went about killing his muggle relatives during a summer between school years.
Tom was, of course, quite terrified of dying at a young age from a bomb being dropped on him, so he used Myrtle's accidental death by the basilisk to make his first horcrux and the deaths of his muggle relatives to make his second. Tom also hoped that by making himself immortal that he'd be able to ensure he met his soulmate. He didn't want to be one of those unfortunate people who never met their soulmate or only got to know them for a short while because one of them died.
After graduating from Hogwarts, Tom worked at Borgin and Burkes for a while and obtained two more vessels to make into horcruxes. He then travelled for many years, eventually finding Ravenclaw's diadem, and made more horcruxes. He learned different languages and a great deal of magic, mostly dark, and interacted with all sorts of different people and creatures.
Tom truly became Lord Voldemort in time, and concern over killing his soulmate was diminished by his creation of the horcruxes and by his increased kill count. After spending so many years of life with no luck in finding his soulmate, he began to suspect that either he killed his soulmate already or he wasn't meant to have a soulmate. Perhaps the implication of having the killing curse on his arm meant that his "soulmate" was essentially death and that he complemented death by being immortal and thus life. Perhaps the killing curse was meant to be a way for life to send gifts to death.
Lord Voldemort was more than just a little surprised when the killing curse not only failed to kill Harry Potter but also backfired. Most of the world assumed that Harry just had some sort of special magical ability that allowed him to defeat He-Who-Must-Not-Be-Named as an infant while Dumbledore believed it was Lily Potter's love for her son that protected Harry from Voldemort. The reality was simply that soulmates cannot kill each other. Lord Voldemort didn't know, just like how he didn't know how horcruxes would negatively affect him; he didn't do enough research on the subjects.