Yechida is one of five levels of the soul often described in the teachings of Chassidus, which were only revealed about 250 years ago - which is likely when the concept (named as such) became mainstream. The five levels of the soul are mentioned in Midrash Rabba (Bereishis 14:9, Devorim 2:37), written in the 4th - 5th century - the earliest source I could find. Although not explicitly mentioned in Tanach, it is connected with a verse in Psalms (22:21):
הצילה מחרב נפשי מיד כלב יחידתי
Save my soul from the sword, my "Yechida" from the grip of the dog.
The Lubavitcher Rebbe explains in Kuntres Inyona Shel Toras Hachasidus (in English "On the Essence of Chassidus") that the five levels of the soul correspond with the five levels in Torah: Peshat, Remez, Drush, Sod and Chassidus. Thus, on one occasion the Zohar does not even list Yechida when enumerating the levels of the soul, and the Midrash just brings it in passing. It is specifically in the teaching of Chassidus that the concept is explained.