The Makor is in Zohar (the first time the words are found is in Sefer Habair). However, it seems like it wasn’t used as a technical term until later by the early Mekubalim. One source says the term’s first usage by the early Mekubalim is by Rabbi Azriel ben Menachem of Gironda.
This is from the Jewish Virtual Library
EIN-SOF (Heb. אֵין סוֹף; "The Infinite," lit. that which is boundless), name given in Kabbalah to God transcendent, in His pure essence: God in Himself, apart from His relationship to the created world. Since every name which was given to God referred to one of the characteristics or attributes by which He revealed Himself to His creatures, or which they ascribed to Him, there is no name or epithet for God from the point of view of His own being. Consequently, when the kabbalists wanted to be precise in their language they abstained from using names like Elohim, the Tetragrammaton, "the Holy One, blessed be He," and others. These names are all found either in the Written or the Oral Law. The Torah, however, refers only to God's manifestations and not to God's own being which is above and beyond His relationship to the created world. Therefore, neither in the Bible, nor in rabbinic tradition was there a term which could fulfill the need of the kabbalists in their speculations on the nature of God. "Know that Ein-Sof is not alluded to either in the Pentateuch, the Prophets, or the Hagiographa, nor in the writings of the rabbis. But the mystics had a vague tradition about it" (Sefer Ma'arekhet ha-Elohut). The term Ein-Sof is found in kabbalistic literature after 1200. However, it was apparently not coined as a technical term since this was not the style in which, in the medieval period, negative terms were coined. Most probably its source is to be found in those phrases stressing God's sublimity which is infinite (ad le-ein sof), or which emphasize the characteristics of the (Divine) thought, comprehension of which "has no end" (ad le-ein sof). The use of this epithet in early kabbalistic literature proved without doubt that the term grew out of this kind of expression. It originated, apparently, in the circle of *Isaac the Blind, and his disciples. In the view of some kabbalists, the name Ein-Sof was likewise applicable to the first product of emanation, the Sefirah Keter, because of its completely concealed nature, and this double use of the word gave rise in kabbalistic literature to considerable confusion. There is no doubt that from the beginning the intention was to use the name in order to distinguish the absolute from the Sefirot which emanated from Him. The choice of this particular name may be explained by the emphasis placed on the infinity of God in the books of *Saadiah Gaon which had a great influence on the circle of the Provençal kabbalists. The term also shows that the anthropomorphic language in which the kabbalists spoke of the living God of faith and revelation does not represent the totality of their theosophical theological approach. At first there was no definite article used in conjunction with Ein-Sof, and it was treated as a proper name, but after 1300 there were kabbalists who spoke of "the Ein-Sof." At first, the term was used only rarely (even in the principal part of the *Zohar its occurrence is very rare), but from about 1300 its use became habitual, and later Kabbalah even speaks of several "kinds of Ein-Sof," e.g., the enveloping Ein-Sof, the enveloped Ein-Sof, the upper Ein-Sof.
BIBLIOGRAPHY:
G. Scholem, Ursprung und Anfaenge der Kabbala (1962), 233–8. ADD. BIBLIOGRAPHY: M. Idel, "The Image of Man above the Sefirot," in: Daat, 4 (1980), 41–55 (Heb.); idem, "Al Torat ha-Elohut be-Reshit ha-Kabbalah," in: Shefah Tal: Studies in Jewish Thought and Culture Presented to Berakhah Sack (2004), 131–48.
Hebrew Wikipedia is more thorough:
הזוהר כמעט אינו מתייחס לאל הנעלם, והוא מוזכר רק בשם אחד בלבד, המיוחד לו: "אין סוף". כינוי זה הופיע לראשונה בחוגו של רבי יצחק סגי נהור בן הראב"ד ותלמידיו שפעלו במאה השתים עשרה ובראשית המאה השלוש עשרה בפרובאנס ובספרד. יש לציין כי המושג "אין סוף" הופיע גם קודם לכן, בספר הבהיר - שם הוא אינו מובא עדיין כשם עצם אלא בהוראת תואר הפועל: "כך המחשבה שאתה תחשוב לאין סוף ותכלית"[8] -, ובתנ"ך - כחלק מתיאור נפלאות מעשיו של האל: "עושה גדלות ואין חקר, נפלאות עד אין מספר"[9].
