This is when the story event to unlock Yukiko’s Social Link stat occurs.
Nothing you do can improve or hinder your ability to date Yukiko before this event occurs. Possessing the Priestess Persona improves the effectiveness of any interactions you have with Yukiko.
Some calendar-specific dates can only be completed with one character. As with most aspects of an RPG like this, there are pros and cons to leveling Social Links.Players cannot start working on improving her Social Link to date her until after an event in the storyline.