Justification, literally, is to be made righteous (or just) in the eyes of God. It is simultaneously, the process of Sanctification. Being made right in the eyes of God, we are made holy. Sanctified.
The entire process begins, in my opinion, with the process of "sanctification". Turning to and seeking God. At this point, one begins to seek justification but has already begun the process of sanctification because in seeking God, one acts in a holy manner.