Matthew Drake was a member of a traveller community in America made up solely of clear-sighted mortals. They moved around America on the hunt for some clue to the Greek Gods' existence. Matthew himself was an 17-year-old college dropout when he met Hecate. They met when he strayed from the place where they'd settled at the time and stumbled across one of Hecate's laborotories. Sensing an intrusion, she teleported there from Olympus and appeared before Matthew's eyes. Noticing that he could see her, she became interested in him and, instead of vaporising him instantly, she began to chat to him, all the while slowly dosing him with love potion. Eventually, she got her wish and the two had intercourse, before she disappeared and sent Matthew away, with him waking up outside the caravans the next day. 6 months later, Matthew awoke to find a baby beside his bed with only a note, a bronze bracelet and a recipe book, filled with recipes for common potions.
Growing up, the baby, now christened Andrew, was the center of attention for the community, as he was a direct link to the gods. The letter that came with him explained that Hecate was his mother and told of Camp Half-Blood, with a command to send Andrew there when he was Matthew's age, in order to protect him. His father actually tried to distance himself from Andrew as much as he could, as the sexual encounter occured against Matthew's will so he had no idea how to feel. Although the nature of being in a travelling community denied Andrew the chance of a substantial education, he constantly studied books in an effort to be as knowledgable as he could and have knowledge that others didn't. He also read the potion book constantly too, but was too afraid to actually try making potions in case something disastrous happened.
When Andrew was 13, his first monster attack occured. He was out gathering firewood from a nearby forest when a harpy flew in towards him. It knocked him to the ground. As he fell, he knocked the bronze bracelet, which he wore everywhere, and it broke open. The surprising thing though was that it then morphed into a sword. On instinct, he picked it up and waited for the harpy to fly again. As it did, he plunged his sword upwards through it's stomach, killing it instantly but earning a cut on his back for his troubles. When he returned to the community, he quickly filled everyone in on what happened. He knew he needed to be prepared and, with their help, he consulted the book in order to make a simple noise potion using household ingredients that they gathered for him so that he could distract the next monster and buy himself time.
The potion was not required until the year after, when he was attacked by a flock of stymphalian birds. This time though, he saw them from a distance and threw his noise potion at one of the three monsters. However, it missed horrendously and hit the ground below. Fortunately, stymphalian birds turn out to be extremely vulnerable to loud noises and just hearing it from a distance caused all three to crash in a daze. From there, it was easy for Andrew to get close enough to decapitate each of them, killing them all. That encounter taught Andrew the usefulness of potions and being prepared and from then on he constantly carried potions on his person, along with studying monsters and their weaknesses. This helped in his next attacks. When he was 15, a myrmeke was disabled by a potion that glued its mouth together, preventing it from spitting acid or using it's mandibles. From there it was a simple task of puncturing its belly and killing it. When he was 16, he killed a scythian draconae by using a potion to summon a smokescreen and then sneaking up behind it and killing it.
By the time he reached 17, his community had gotten close enough to Camp Half-Blood for Andrew to make it there alone. After being there a few days, he was officially claimed by Hecate and resides there full-time.