(Exodus 19:1:) IN THE THIRD MONTH. The Torah is threefold, and its letters are threefold, and the patriarchs are threefold, and the tribe through whose hand it was given is threefold, and Moses was {threefold among them} [the third among them], and the letters of his name are threefold, and the siblings were three, and he was hidden for three months — [and on the third day, and in the third month]. The Torah is threefold: Torah, Prophets, and Writings. And its letters are threefold: alef, bet, gimel. The patriarchs are threefold: Abraham, Isaac, and Jacob. And Moses was the third among them, as it is said (Deuteronomy 5:5), "I stood between the LORD and you." And the letters are threefold: Moses [Mem, Shin, He]. And he was from the third tribe: Reuben, Simeon, and Levi. And the siblings were three: Moses, Aaron, and Miriam. And he was hidden for three, as it is said (Exodus 2:2), "And she hid him three months." And on the third day, as it is said (Exodus 19:11), "For on the third day the LORD will come down," and so forth. [And in the third month, as it is said: In the third month.]
Why the Torah Was Given in the Threefold Third Month at Sinai
Midrash Tanchuma Buber, Yitro 8:1
בחדש השלישי. התורה משולשת, ואותיותיה משולשות, והאבות משולשין, והשבט שניתנה על ידו משולש, ומשה (משולש מביניהם) [שלישי ביניהם], ואותיותיו משולשין, ואחים שלשה, ונצפן לג' ירחים [וביום השלישי, ובחדש השלישי], התורה משולשת תורה נביאים וכתובים, ואותיותיה משולשות אלף בית גימל, האבות משולשין אברהם יצחק ויעקב, ומשה שלישי ביניהם אנכי עומד בין ה' וביניכם (דברים ה ה), ואותיות משולשות משה, ומשבט שלישי ראובן שמעון ולוי, ואחים שלשה משה אהרן ומרים, ונצפן לג' ותצפנהו שלשה ירחים (שמות ב ב), וביום השלישי כי ביום השלישי ירד ה' וגו' (שם יט יא), [ובחדש השלישי שנאמר בחדש השלישי].