One who is actually very fortunate can begin Krsna consciousness, as stated by Caitanya Mahaprabhu to Srila Rupa Gosvami:

There are millions of living entities who have become conditioned by the laws of material nature, and they are wandering throughout the planetary systems of this universe in different bodily forms. Among them, one who is fortunate meets a bona fide spiritual master by the grace of Krsna and comes to understand the meaning of devotional service. By discharging devotional service under the direction of the bona fide spiritual master, or acarya, he develops love of Godhead. One whose love of Godhead (krsna-prema) is awakened and who thus becomes a devotee of the inconceivable Supreme Personality of Godhead is to be considered extremely fortunate. The Mayavadi sannyasis admitted this fact to Sri Caitanya Mahaprabhu. It is not easy for one to become a Krsna conscious person, but by the mercy of Sri Caitanya Mahaprabhu it can be possible, as will be proven in the course of this narration.