The vision of a future era in which all knowledge of Hashem will be universal and direct is grounded in Yeshayahu 11:9, which declares that the earth will be filled with knowledge of Hashem as water covers the sea, and the Sulam on Zohar, Vayikra 388 reads this together with the prophecy of Yirmiyahu — 'they shall no longer teach one another saying know Hashem, for all of them shall know Me' — as the Zohar's promise that in the time of Mashiach the Holy One will reveal the deepest secrets of Torah.
זהר, זהר חדש בראשית ויצא מ, וראה שם עוד similarly teaches that one who engages in Torah each day has deep supernal secrets renewed for him — the Torah itself says to such a person 'I will give you to drink from spiced wine, from the juice of my pomegranates' — and identifies this 'preserved wine' with matters destined to be revealed to the righteous in the time to come.
Peri Tzadik, Rosh Chodesh Sivan 2:1 draws on Shir HaShirim directly (the verse 'יִשָּׁקֵנִי') to describe how at Matan Torah, when Israel heard the first of the Ten Commandments, Torah was implanted in their hearts and they grasped the full taste of Torah she-be'al peh — a state he compares explicitly to what will obtain in the future, when 'they shall no longer teach' because all will know Hashem from within.
Esh Kodesh, Jewish Year 5700, Shavuot adds that the giving of the Torah was itself an act of divine teaching — Hashem taught Israel the Ten Commandments directly — and notes a Midrashic tradition that Israel responded 'yes' to the positive commands and 'no' to the prohibitions, situating the first dibros as the paradigmatic instance of Hashem as direct teacher of His people.