Alcock was born in Winnipeg, Manitoba. He holds a Bachelor of Arts degree from Simon Fraser University and a Master's Degree in Public Administration from Harvard University. He was the director of Manitoba Child and Family Services from 1983 to 1985 and in this capacity spearheaded an effort to rewrite the province's child protection legislation. As a result of his efforts, Manitoba became the first province in Canada to introduce official protocols to deal with instances of child sex abuse. Alcock has also been active with the Harvard Policy Group, which studies the effects of Information Technology on the public sector. He began his political career at the provincial level, working as an organizer for the Manitoba Liberal Party in the early 1980s.