Snoke: "I have never had a student with such promise-before you"
Kylo: "It is your teaching that make me strong, Supreme Leader."
Snoke: "It is far more than that. It is where you are from. What you are made of. The dark side, and the light. The finest sculptor cannot fashion a masterpiece from poor materials. He must have something pure, something strong, something unbreakable, with which to work. I have you."
Snoke: "Kylo Ren, I watched the Galactic Empire rise, and then fall. The gullible prattle on about the triumph of truth and justive, of individualism and free will. As if such things were solid and real instead of simple subjective judgements. The historians have it all wrong. It was neither poor strategy nor arrogance that brought down the empire. You know too well what did."
Kylo: "Sentiment"
Snoke: "The elements align, Kylo Ren. You alone are caught in the wings of the storm. Your bond is not just to Vader, but to Skywalker himself. Leia..."
And then later in the book;
Leia: He knew our child would be strong with the Force. That he was born with equal potential for good or evil.
Han: "You knew this from the beginning? Why didn't you tell me?"
Leia: "Many reasons. I was hoping that I was wrong, that it wasn't true. I hoped I could sway him, turn him away from the dark side, without having to involve you. You had, you gave, wonderful qualitied Han, but patience and understanding were never among them. I was afraid your reactions would only drive him father to the dark side. I thought I could shield him from Snoke's influence and you from what was happening."
Han: "So Snoke was watching our son."
Leia: Always. From the shadows, in the beginning, even before I realized what was happening, he was manipulating everything, pulling our son toward the dark side."
So basically Snoke targeted him as a young boy to corrupt, and then did so. Or at least began to.